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  • 1
    ISSN: 1436-4646
    Keywords: Geometric Programming ; Code Comparisons ; Numerical Testing ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.
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  • 2
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    Mathematical programming 23 (1982), S. 75-86 
    ISSN: 1436-4646
    Keywords: Constrained Optimization ; Global Convergence ; Nonlinear Programming ; Penalty Function ; Quasi-Newton Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved.
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  • 3
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    Mathematical programming 22 (1982), S. 82-92 
    ISSN: 1436-4646
    Keywords: Generic Programming ; Optimality Conditions ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Optimality conditions for families of nonlinear programming problems inR n are studied from a generic point of view. The objective function and some of the constraints are assumed to depend on a parameter, while others are held fixed. Techniques of differential topology are used to show that under suitable conditions, certain strong second-order conditions are necessary for optimality except possibly for parameter values lying in a negligible set.
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  • 4
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    Mathematical programming 24 (1982), S. 137-161 
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we motivate and describe an algorithm to solve the nonlinear programming problem. The method is based on an exact penalty function and possesses both global and superlinear convergence properties. We establish the global qualities here (the superlinear nature is proven in [7]). The numerical implementation techniques are briefly discussed and preliminary numerical results are given.
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  • 5
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    Mathematical programming 24 (1982), S. 123-136 
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Exact Penalty Methods ; Successive Quadratic Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we consider the final stage of a ‘global’ method to solve the nonlinear programming problem. We prove 2-step superlinear convergence. In the process of analyzing this asymptotic behavior, we compare our method (theoretically) to the popular successive quadratic programming approach.
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  • 6
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    Applied physics 27 (1982), S. 167-169 
    ISSN: 1432-0630
    Keywords: 61.70 ; 68 ; 74
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A simple method is presented to prepare very low pinning niobium foils on which geometrically well defined Nb3Sn-pinning structures of arbitrary shape are deposited. This facilitates the fabrication of samples for guided vortex motion experiments some of which are reported.
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  • 7
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    Applied physics 28 (1982), S. 99-102 
    ISSN: 1432-0630
    Keywords: 61.70 ; 81.40
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Supersaturated surface alloys produced by very high dose (0.8−2.6×1017cm−2) implantation of As-ions into silicon and subsequent pulsed electron-beam annealing have been investigated by means of the channeling technique. The maximum solubility limit of 7×1021 As/cm3 has been determined. It exceeds the equilibrium solubility limit by more than a factor of 4. Angular scan measurements indicated that for doses above 1×1017cm−2 As atoms are displaced by about 0.12 Å from the regular lattice sites.
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  • 8
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    Applied physics 28 (1982), S. 179-187 
    ISSN: 1432-0630
    Keywords: 78.70 ; 61.70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Positron annihilation measurements of the coincidence count rate at the peak of the angular correlation curve (CCR) have been performed as a function of temperature for the alloy systemFeTi in a concentration range up to about 1.3 at. %. The concentration dependence of the effective vacancy formation enthalpy (H 1V F )eff suggests the existence of an attractive interaction between vacancies and the impurity atoms. It will be shown that the description of the vacancy concentration in an alloy according to the Lomer model is not valid in this case, because it neglects binding of vacancies to solute atom pairs and to higher agglomerates. The application of a model proposed by Dorn and Mitchell gives evidence that beyond the binding of a vacancy to a single solute atom in the concentration range investigated also aggregates of a vacancy bound to two and three foreign atoms must be taken into account. The analysis of the measurements according to the method of Hehenkamp and Sander gives values for the respective vacancy-solute-atom(s) binding enthalpies H 1 B =0.25eV, H 2 B =0.53eV and H 3 B =0.91eV. The discussion of the temperature and solute-atoms concentration dependence of the vacancy concentration suggests a much more complicated behaviour than for pure metals even at low solute-atom concentrations.
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  • 9
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    Applied physics 27 (1982), S. 257-261 
    ISSN: 1432-0630
    Keywords: 78.70 ; 61.70 ; 81
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The positron lifetime was measured in cadmium in the temperature range between 80 K and 500 K. For the first time a plateau was observed by this method in polycrystalline samples. The obtained data are well explained by depletion of shallow traps forT≤180 K and by self-trapping in the prevacancy region.
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  • 10
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    Applied physics 29 (1982), S. 105-111 
    ISSN: 1432-0630
    Keywords: 71.55F ; 61.70 ; 73.40Q
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The annealing behavior of trap-centers was studied in float-zone silicon wafers containing A-swirl defects. Samples from areas of high and low A-swirl density were annealed in nitrogen ambient between 100° and 900 °C, and analysed using the Deep Level Transient Spectroscopy. The results indicate, that two levels atE c }-0.07 eV,σ n=4.6×10−16 cm2, andE c−0.49eV,σ n=6.6×10−16cm2 are caused by one defect, for which the silicon di-selfinterstitial is a likely interpretation. A level atE c }-0.11 eV was assigned to interstitial carbon. Both defects annealed out at about 170 °C. After 600 °C annealing an additional level atE c−0.2 eV was detected, which was attributed to an interstitial silicon carbon complex. Heat treatment at 800 °C generated a new level atE c−0.49 eV,σ n=2.9×10−16cm2 only in the area of high A-swirl defect density. This level was also observed after oxidation and subsequent annealing of silicon.
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  • 11
    ISSN: 1432-0630
    Keywords: 61.70 ; 78.70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Trapping of positrons at vacancy-type defects in magnesium was studied by positron lifetime and Doppler-broadening measurements. Vacancy defects were produced by quenching, electron irradiation and deformation at low temperatures as well as by thermal agitation at elevated temperatures. In the first three cases we observed trapping at multiple vacancies, which anneal out between 77...400 K. Thermal equilibrium measurements show S-shape behaviour originating from positron trapping at magnesium monovacancies. However, changes in the positron parameters were very small, which is due to the weakness of the positron-vacancy interaction. A detrapping analysis yielded a positron-vacancy binding energy of the order of 0.3...0.4 eV.
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  • 12
    ISSN: 1432-0630
    Keywords: 61.70 ; 78.70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Positron-annihilation lineshape parameter measurements were performed during isothermal annealing of room temperature deformed iron. An isothermal annealing effect is seen in impure iron while in pure iron no effect is measured.
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  • 13
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    Applied physics 27 (1982), S. 149-152 
    ISSN: 1432-0630
    Keywords: 78.70 ; 61.70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract A simple model is developed for the trapping of positrons at grain boundaries. It is shown that there is a linear relationship between any linear annihilation parameter and the inverse grain size. An effective grain boundary width is defined, which depends on the positron diffusion length and on the strength of the grain boundary for positrons. The effect of detrapping on this effective width is also considered. The model is tested by using the experimental results available in the literature.
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  • 14
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    Applied physics 27 (1982), S. 171-176 
    ISSN: 1432-0630
    Keywords: 61.70 ; 66 ; 85.30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The paper presents a theoretical study of the diffusion of gold into dislocated silicon wafers in terms of the kick-out mechanism Au i ⇄Au s +I, where Au i , Au s , andI mean Au interstitials, substitutional Au atoms, and Si self-interstitials, respectively. In agreement with experiments it is found that the Au s concentration in the centre of a wafer,C s m , increases with the durationt of the diffusion anneal according toC s m =C s eq (k 0 t)1/2 except forC s m values in the vicinity of the solubility limitC s eq of Au s . Approximate analytical expressions fork 0 as a function of the densityN I of the dislocations acting asI sinks are given for the entire regime 0≦NI〈+t8.
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  • 15
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    Applied physics 29 (1982), S. 199-200 
    ISSN: 1432-0630
    Keywords: 61.70
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract Conditions are discussed under which an interstitial atom absorbed in the core of a gliding 60° dislocation belonging to the glide set can be transformed into an antisite defect. The mechanism considered may be responsible for an increase in the concentration of AsGa defects observed in GaAs single crystals after their plastic deformation.
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  • 16
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    Applied physics 28 (1982), S. 79-92 
    ISSN: 1432-0630
    Keywords: 61.70 ; 66.30 ; 85.30
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract The information available on the diffusion of oxygen and on the formation of thermal donors in silicon is critically reviewed. In this context the effects of intrinsic point defects on the diffusion-controlled growth of oxygen precipitates is investigated in some detail. Seemingly contradictory experimental results on the diffusivity of oxygen in silicon at temperatures around 400° C are explained in terms offast-diffusing gas-like molecular oxygen in silicon. The concept of molecular oxygen is also invoked in a newly suggested model of thermal donor formation in silicon. The diffusivity of molecular oxygen in silicon is estimated to be around 10−9cm2s−1 at 450° C, almost nine orders of magnitude higher than the diffusivity of atomic oxygen in interstitial position.
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  • 17
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    Mathematical geology 14 (1982), S. 309-319 
    ISSN: 1573-8868
    Keywords: Bias ; drift ; semivariogram ; geostatistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract When nonlinear drift is present, the nature of the bias in the experimental semivariogram estimator of the semivariogram function is determined by the extent and density of the sampling as well as by the drift function itself. The bias caused by drift may affect the interpretation of the experimental semivariogram over its entire range.
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  • 18
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    Mathematical geology 14 (1982), S. 645-660 
    ISSN: 1573-8868
    Keywords: geostatistics ; uranium ; production forecast
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Geostatistical estimation techniques were customized to allow forecasting of production figures at the Silver Bell uranium mine (Uravan District).Surface drill hole data were used to provide a block model of kriged estimators of average uranium grades. Figures for recoverable ore grade and the ore-waste ratio are then deduced from regressive curves previously obtained from underground information and production data. Cross-validations of the entire model were performed and were found positive.
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  • 19
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    Mathematical geology 14 (1982), S. 87-106 
    ISSN: 1573-8868
    Keywords: coal ; geostatistics ; kriging ; regional estimation ; systematic sampling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Two-dimensional systematic sampling of small plots followed by the kriging of those plots may be employed to obtain regional estimates of coal resources and measures of the accuracy of the estimates. The use of sampling makes large savings in computation possible. Two case studies involving the estimation of coal tonnage are discussed.
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  • 20
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    Mathematical geology 14 (1982), S. 57-64 
    ISSN: 1573-8868
    Keywords: estimation ; generalized covariance function ; generalized increments ; geostatistics ; intrinsic random functions ; multicollinearity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The estimation of the generalized covariance function, K, is a major problem in the use of intrinsic random functions of order k to obtain kriging estimates. The precise estimation by least-squares regression of the parameters in polynomial models for K is made difficult by the nature of the distribution of the dependent variable and the multicollinearity of the independent variables.
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  • 21
    ISSN: 1573-8868
    Keywords: geostatistics ; variogram ; outliers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Variograms for gold and lead values from the Loraine and Prieska mines, respectively, indicate that data outliers can seriously distort and/or mask the real variogram patterns. Studies show that this problem is best overcome for these mines by logarithmic transformation of the data, and/or a suitable screening out of such outliers, and/or more robust variogram estimation procedures; the benefits are particularly significant when the basic data is limited.
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  • 22
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    Mathematical geology 14 (1982), S. 217-239 
    ISSN: 1573-8868
    Keywords: geostatistics ; variograms ; anisotropies ; tungsten
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract The regionalization of tungsten grades at the χ deposit represents an ideal case for anisotropic hole-effect variogram modeling. The modeling technique is presented step by step and the consequences of the model on block kriging are indicated.
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  • 23
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    Mathematical geology 14 (1982), S. 387-404 
    ISSN: 1573-8868
    Keywords: geostatistics ; resource estimation ; geoexploration ; sampling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Sampling exploration of uncertain functions to locate critical contour levels is most effective if sampling decisions are made sequentially. A simple sequential exploration strategy, based on pseudo-Bayesian second-moment analysis, is proposed and compared with non-sequential systematic sampling. Repeated application to functions simulated pseudorandomly from stationary random processes on the line and on the plane indicates uniform superiority of the sequential strategy. The method is particularly advantageous when the function of interest,h(X), has an uncertain trend, and in general when the random process that quantifies prior uncertainty onh(X) is highly correlated.
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  • 24
    ISSN: 1573-8868
    Keywords: geostatistics ; kriging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Parallel variogram analyses, block kriging, and follow-up studies were effected for the lead content of part of the Prieska copper-zinc ore body and for the gold content of the highly variable Breef in a section of the Loraine gold mine, based first on untransformed values and second on logarithmically transformed values using the lognormal-de Wijsian model. For both models the effect was also analyzed of using the population mean or ignoring it. Practical follow-up comparisons confirm theoretical considerations and show that on these mines conditional biases can be eliminated conveniently by kriging with mean; also that the lognormal-de Wijsian model with mean gives the best results.
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  • 25
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    Journal of optimization theory and applications 38 (1982), S. 83-96 
    ISSN: 1573-2878
    Keywords: Numerical methods ; multiple shooting method ; optimal control ; aircraft trajectories ; flight mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Three-dimensional minimum-time 180° turns of a fighter aircraft are computed for several initial velocitiesV 0 and altitudesh 0. It is shown that the optimum turns consist of split -S maneuvers forV 0≦V 10, three-dimensional maneuvers forV 10〈V 0〈V 20, and half-loops forV 0≧V 20, withV 10,V 20 being functions of altitude or thrust/weight ratio.
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  • 26
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    Journal of optimization theory and applications 37 (1982), S. 251-275 
    ISSN: 1573-2878
    Keywords: Economics ; political cycles ; discrete dynamic systems ; dynamic programming ; optimal control ; Poincaré mapping ; Stieltjes matrix ; optimization in Hilbert space ; infinite horizon ; turnpike theorem
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Under the hypothesis of a myopic electorate, vote-loss-minimizing behavior by the party in power, subject to a dynamic inflation-unemployment relation, is shown to generate an attractive, stable electoral policy cycle. The model presented is derived, with some improvements, from the analogous models of MacRae and Nordhaus. Furthermore, an attempt is made to specify the mathematical aspects of the problem by the Poincaré mapping.
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  • 27
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    Journal of optimization theory and applications 38 (1982), S. 111-135 
    ISSN: 1573-2878
    Keywords: Minimax problems ; minimax function ; minimax function depending on the state ; minimax function depending on the control ; optimal control ; minimax optimal control ; numerical methods ; computing methods ; transformation techniques ; gradient-restoration algorithms ; sequential gradient-restoration algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In a previous paper (Part 1), we presented general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We considered two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P). In this paper, the transformation techniques presented in Part 1 are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. Both the single-subarc approach and the multiple-subarc approach are employed. Three test problems characterized by known analytical solutions are solved numerically. It is found that the combination of transformation techniques and sequential gradient-restoration algorithm yields numerical solutions which are quite close to the analytical solutions from the point of view of the minimax performance index. The relative differences between the numerical values and the analytical values of the minimax performance index are of order 10−3 if the single-subarc approach is employed. These relative differences are of order 10−4 or better if the multiple-subarc approach is employed.
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  • 28
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    Journal of optimization theory and applications 38 (1982), S. 97-109 
    ISSN: 1573-2878
    Keywords: Minimax problems ; minimax function ; minimax function depending on the state ; minimax function depending on the control ; optimal control ; minimax optimal control ; numerical methods ; computing methods ; transformation techniques ; gradient-restoration algorithms ; sequential gradient-restoration algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P). For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector π, as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized. For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector π, as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized. In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.
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  • 29
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    Journal of optimization theory and applications 36 (1982), S. 409-417 
    ISSN: 1573-2878
    Keywords: Optimal design ; optimal control ; dynamic systems ; gantry cranes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Problems arising in the optimal control of gantry crane instaliations are considered. Continuous controls to minimize a control squared objective function are obtained. The amplitude of in-plane oscillations of the suspended mass is assumed small. The optimal controls are sufficiently simple for practical realization.
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  • 30
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    Journal of optimization theory and applications 36 (1982), S. 521-534 
    ISSN: 1573-2878
    Keywords: Darboux points ; global optimality ; conjugate points ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The question of the existence and the location of Darboux points (beyond which global optimality is lost) is crucial for minimal sufficient conditions for global optimality and for computation of optimal trajectories. Here, we investigate numerically the Darboux points and their relationship with conjugate points for a problem of minimum fuel, constant velocity, horizontal aircraft turns to capture a line. This simple second-order optimal control problem shows that ignoring the possible existence of Darboux points may play havoc with the computation of optimal trajectories.
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