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  • Articles  (11)
  • Nonlinear programming  (11)
  • 1975-1979  (11)
  • 1945-1949
  • 1977  (8)
  • 1975  (3)
  • Mathematics  (11)
  • Sociology
  • Architecture, Civil Engineering, Surveying
Collection
  • Articles  (11)
Source
Keywords
Publisher
Years
  • 1975-1979  (11)
  • 1945-1949
Year
Topic
  • Mathematics  (11)
  • Sociology
  • Architecture, Civil Engineering, Surveying
  • Computer Science  (3)
  • 1
    Electronic Resource
    Electronic Resource
    The use of augmented lagrangian functions for sensitivity analysis in nonlinear programming (1977)
    Springer
    Mathematical programming 12 (1977), S. 281-284 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear programming ; Augmented Lagrangian functions ; Sensitivity analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01593794
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  • 2
    Electronic Resource
    Electronic Resource
    New algorithms for constrained minimax optimization (1977)
    Springer
    Mathematical programming 13 (1977), S. 140-155 
    Details
    ISSN: 1436-4646
    Keywords: Minimax optimization ; Nonlinear programming ; Computer-aided network design
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A constrained minimax problem is converted to minimization of a sequence of unconstrained and continuously differentiable functions in a manner similar to Morrison's method for constrained optimization. One can thus apply any efficient gradient minimization technique to do the unconstrained minimization at each step of the sequence. Based on this approach, two algorithms are proposed, where the first one is simpler to program, and the second one is faster in general. To show the efficiency of the algorithms even for unconstrained problems, examples are taken to compare the two algorithms with recent methods in the literature. It is found that the second algorithm converges faster with respect to the other methods. Several constrained examples are also tried and the results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584333
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  • 3
    Electronic Resource
    Electronic Resource
    Simplicial decomposition in nonlinear programming algorithms (1977)
    Springer
    Mathematical programming 13 (1977), S. 49-68 
    Details
    ISSN: 1436-4646
    Keywords: Algorithm ; APL-code ; Barycentric representation ; Decomposition ; Nonlinear programming ; Pseudo-concave objective ; Simplex
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Simplicial decomposition is a special version of the Dantzig—Wolfe decomposition principle, based on Carathéodory's theorem. The associated class of algorithms has the following features and advantages: The master and the subprogram are constructed without dual variables; the methods remain therefore well-defined for non-concave objective functions, and pseudo-concavity suffices for convergence to global maxima. The subprogram produces affinely independent sets of feasible generator points defining simplices, which the master program keeps minimal by dropping redundant generator points and finding maximizers in the relative interiors of the resulting subsimplices. The use of parallel subspaces allows the direct application of any unrestricted optimization method in the master program; thus the best unconstrained procedure for any type of objective function can be used to find constrained maximizers for it. The paper presents the theory for this class of algorithms, the APL-code of a “demonstration” method and some computational experience with Colville's test problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584323
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  • 4
    Electronic Resource
    Electronic Resource
    Generalized Lagrange multiplier technique for nonlinear programming (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 121-135 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; max-min problems ; Lagrange multiplier technique ; Newton's method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Our aim here is to present numerical methods for solving a general nonlinear programming problem. These methods are based on transformation of a given constrained minimization problem into an unconstrained maximin problem. This transformation is done by using a generalized Lagrange multiplier technique. Such an approach permits us to use Newton's and gradient methods for nonlinear programming. Convergence proofs are provided, and some numerical results are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932516
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  • 5
    Electronic Resource
    Electronic Resource
    Square-root variable-metric methods for minimization (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 251-259 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; variable-metric methods ; parameter optimization ; function minimization ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Variable-metric methods are presented which do not need an accurate one-dimensional search and eliminate roundoff error problems which can occur in updating the metric for large-dimension systems. The methods are based on updating the square root of the metric, so that a positive-definite metric always results. The disadvantage of intentionally relaxing the accuracy of the one-dimensional search is that the number of iterations (and hence, gradient evaluations) increases. For problems involving a large number of variables, the square-root method is presented in a triangular form to reduce the amount of computation. Also, for usual optimization problems, the square-root procedure can be carried out entirely in terms of the metric, eliminating storage and computer time associated with computations of the square root of the metric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933529
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  • 6
    Electronic Resource
    Electronic Resource
    An economical method of calculating Lagrange multiplier estimates for nonlinear programming problems when many of the constraints are bounds on the variables (1977)
    Springer
    Journal of optimization theory and applications 21 (1977), S. 235-239 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; computing methods ; Lagrange multiplier estimates ; bounded variables ; large-scale problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Some recent methods for solving nonlinear programming problems make use of estimates of the Lagrange multipliers. These estimates are usually calculated by solving a system oft linear equations, wheret is the number of active constraints. It is shown that, when a large proportion of the active constraints consists of simple upper or lower bounds on the variables, then computational effort can be saved by means of a reorganization of this linear system.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932523
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  • 7
    Electronic Resource
    Electronic Resource
    A globally convergent method for nonlinear programming (1977)
    Springer
    Journal of optimization theory and applications 22 (1977), S. 297-309 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; global convergence ; exact penalty function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Recently developed Newton and quasi-Newton methods for nonlinear programming possess only local convergence properties. Adopting the concept of the damped Newton method in unconstrained optimization, we propose a stepsize procedure to maintain the monotone decrease of an exact penalty function. In so doing, the convergence of the method is globalized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932858
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  • 8
    Electronic Resource
    Electronic Resource
    On the solution of the unidimensional local minimization problem (1977)
    Springer
    Journal of optimization theory and applications 23 (1977), S. 471-471 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; unidemensional search ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A correction of the procedure of Ref. 1 is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933454
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  • 9
    Electronic Resource
    Electronic Resource
    Iterative determination of parameters for an exact penalty function (1975)
    Springer
    Journal of optimization theory and applications 16 (1975), S. 49-66 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; penalty-function methods ; Lagrange multipliers ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract As an approach to solving nonlinear programs, we study a class of functions known to be exact penalty functions for a proper choice of the parameters. The goal is to iteratively determine the correct parameters. A basic algorithm has been developed. We have proved that this algorithm converges to a global solution for concave programs and, in the limited computational tests performed to date, it has always converged to at least a local solution for nonconcave programs also.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935623
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  • 10
    Electronic Resource
    Electronic Resource
    A class of quadratically convergent algorithms for constrained function minimization (1975)
    Springer
    Journal of optimization theory and applications 16 (1975), S. 447-485 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; mathematical programming ; quadratically convergent algorithms ; conjugate-gradient methods ; variable-metric methods ; computing methods ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of minimizing a functionf(x) subject to the constraint ϕ(x)=0 is considered. Here,f is a scalar,x is ann-vector, and ϕ is anm-vector, wherem 〈n. A general quadratically convergent algorithm is presented. The conjugate-gradient algorithm and the variable-metric algorithms for constrained function minimization can be obtained as particular cases of the general algorithm. It is shown that, for a quadratic function subject to a linear constraint, all the particular algorithms behave identically if the one-dimensional search for the stepsize is exact. Specifically, they all produce the same sequence of points and lead to the constrained minimal point in no more thann −r descent steps, wherer is the number of linearly independent constraints. The algorithms are then modified so that they can also be employed for a nonquadratic function subject to a nonlinear constraint. Some particular algorithms are tested through several numerical examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933853
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  • 11
    Electronic Resource
    Electronic Resource
    A note on the maximum of quasiconcave functions (1975)
    Springer
    Journal of optimization theory and applications 16 (1975), S. 565-569 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear programming ; function maximization ; mathematical programming ; quasiconcave functions ; global maximality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is shown that the class of weakly nonconstant functions possesses the property that every local maximum is global. This is also a necessary condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933860
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