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  • mathematical programming  (3)
  • parameter optimization  (3)
  • Ionosphere (mid-latitude ionosphere; modelling and forecasting)  (2)
  • Springer  (6)
  • American Geophysical Union (AGU)
  • 2000-2004  (2)
  • 1975-1979  (4)
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Keywords
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  • Springer  (6)
  • American Geophysical Union (AGU)
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  • 2000-2004  (2)
  • 1975-1979  (4)
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  • 1
    ISSN: 0992-7689
    Keywords: Atmospheric composition and structure (thermosphere-composition and chemistry) ; Ionosphere (mid-latitude ionosphere; modelling and forecasting)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Annual, seasonal and semiannual variations of F2-layer electron density (NmF2) and height (hmF2) have been compared with the coupled thermosphere-ionosphere-plasmasphere computational model (CTIP), for geomagnetically quiet conditions. Compared with results from ionosonde data from midlatitudes, CTIP reproduces quite well many observed features of NmF2, such as the dominant winter maxima at high midlatitudes in longitude sectors near the magnetic poles, the equinox maxima in sectors remote from the magnetic poles and at lower latitudes generally, and the form of the month-to-month variations at latitudes between about 60°N and 50°S. CTIP also reproduces the seasonal behaviour of NmF2 at midnight and the summer-winter changes of hmF2. Some features of the F2-layer, not reproduced by the present version of CTIP, are attributed to processes not included in the modelling. Examples are the increased prevalence of the winter maxima of noon NmF2 at higher solar activity, which may be a consequence of the increase of F2-layer loss rate in summer by vibrationally excited molecular nitrogen, and the semiannual variation in hmF2, which may be due to tidal effects. An unexpected feature of the computed distributions of NmF2 is an east-west hemisphere difference, which seems to be linked to the geomagnetic field configuration. Physical discussion is reserved to the companion paper by Rishbeth et al.
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  • 2
    ISSN: 0992-7689
    Keywords: Atmospheric composition and structure (thermosphere-composition and chemistry) ; Ionosphere (mid-latitude ionosphere; modelling and forecasting)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The companion paper by Zou et al. shows that the annual and semiannual variations in the peak F2-layer electron density (NmF2) at midlatitudes can be reproduced by a coupled thermosphere-ionosphere computational model (CTIP), without recourse to external influences such as the solar wind, or waves and tides originating in the lower atmosphere. The present work discusses the physics in greater detail. It shows that noon NmF2 is closely related to the ambient atomic/molecular concentration ratio, and suggests that the variations of NmF2 with geographic and magnetic longitude are largely due to the geometry of the auroral ovals. It also concludes that electric fields play no important part in the dynamics of the midlatitude thermosphere. Our modelling leads to the following picture of the global three-dimensional thermospheric circulation which, as envisaged by Duncan, is the key to explaining the F2-layer variations. At solstice, the almost continuous solar input at high summer latitudes drives a prevailing summer-to-winter wind, with upwelling at low latitudes and throughout most of the summer hemisphere, and a zone of downwelling in the winter hemisphere, just equatorward of the auroral oval. These motions affect thermospheric composition more than do the alternating day/night (up-and-down) motions at equinox. As a result, the thermosphere as a whole is more molecular at solstice than at equinox. Taken in conjunction with the well-known relation of F2-layer electron density to the atomic/molecular ratio in the neutral air, this explains the F2-layer semiannual effect in NmF2 that prevails at low and middle latitudes. At higher midlatitudes, the seasonal behaviour depends on the geographic latitude of the winter downwelling zone, though the effect of the composition changes is modified by the large solar zenith angle at midwinter. The zenith angle effect is especially important in longitudes far from the magnetic poles. Here, the downwelling occurs at high geographic latitudes, where the zenith angle effect becomes overwhelming and causes a midwinter depression of electron density, despite the enhanced atomic/molecular ratio. This leads to a semiannual variation of NmF2. A different situation exists in winter at longitudes near the magnetic poles, where the downwelling occurs at relatively low geographic latitudes so that solar radiation is strong enough to produce large values of NmF2. This circulation-driven mechanism provides a reasonably complete explanation of the observed pattern of F2 layer annual and semiannual quiet-day variations.
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 18 (1976), S. 469-483 
    ISSN: 1573-2878
    Keywords: Nonlinear least-square problems ; parameter optimization ; penalty function methods ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An algorithm for solving the general nonlinear least-square problem is developed. An estimate for the Hessian matrix is constructed as the sum of two matrices. The first matrix is the usual first-order estimate used by the Gauss method, while the second matrix is generated recursively using a rank-one formula. Test results indicate that the method is superior to the standard Gauss method and compares favorably with other methods, especially for problems with nonzero residuals at the solution.
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 21 (1977), S. 137-174 
    ISSN: 1573-2878
    Keywords: Augmented penalty function ; method of multipliers ; penalty function methods ; nonlinear programming ; mathematical programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes an accelerated multiplier method for solving the general nonlinear programming problem. The algorithm poses a sequence of unconstrained optimization problems. The unconstrained problems are solved using a rank-one recursive algorithm described in an earlier paper. Multiplier estimates are obtained by minimizing the error in the Kuhn-Tucker conditions using a quadratic programming algorithm. The convergence of the sequence of unconstrained problems is accelerated by using a Newton-Raphson extrapolation process. The numerical effectiveness of the algorithm is demonstrated on a relatively large set of test problems.
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 24 (1978), S. 523-548 
    ISSN: 1573-2878
    Keywords: Multiplier method ; gradient projection method ; penalty function methods ; nonlinear programming ; parameter optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper describes a gradient projection-multiplier method for solving the general nonlinear programming problem. The algorithm poses a sequence of unconstrained optimization problems which are solved using a new projection-like formula to define the search directions. The unconstrained minimization of the augmented objective function determines points where the gradient of the Lagrangian function is zero. Points satisfying the constraints are located by applying an unconstrained algorithm to a penalty function. New estimates of the Lagrange multipliers and basis constraints are made at points satisfying either a Lagrangian condition or a constraint satisfaction condition. The penalty weight is increased only to prevent cycling. The numerical effectiveness of the algorithm is demonstrated on a set of test problems.
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 16 (1975), S. 1-24 
    ISSN: 1573-2878
    Keywords: Penalty-function methods ; mathematical programming ; nonlinear programming ; pseudo Newton-Raphson methods ; parameter optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An effective algorithm is described for solving the general constrained parameter optimization problem. The method is quasi-second-order and requires only function and gradient information. An exterior point penalty function method is used to transform the constrained problem into a sequence of unconstrained problems. The penalty weightr is chosen as a function of the pointx such that the sequence of optimization problems is computationally easy. A rank-one optimization algorithm is developed that takes advantage of the special properties of the augmented performance index. The optimization algorithm accounts for the usual difficulties associated with discontinuous second derivatives of the augmented index. Finite convergence is exhibited for a quadratic performance index with linear constraints; accelerated convergence is demonstrated for nonquadratic indices and nonlinear constraints. A computer program has been written to implement the algorithm and its performance is illustrated in fourteen test problems.
    Type of Medium: Electronic Resource
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