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  • Articles  (7)
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  • nonlinear programming  (7)
  • 1995-1999
  • 1985-1989  (7)
  • 1950-1954
  • 1988  (7)
  • Mathematics  (7)
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  • Books
  • Articles  (7)
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  • 1995-1999
  • 1985-1989  (7)
  • 1950-1954
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  • Mathematics  (7)
  • 1
    Electronic Resource
    Electronic Resource
    On the exactness of a class of nondifferentiable penalty functions (1988)
    Springer
    Journal of optimization theory and applications 57 (1988), S. 399-410 
    Details
    ISSN: 1573-2878
    Keywords: Optimization ; nonlinear programming ; penalty functions ; exact penalty functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of nondifferentiable penalty functions for the solution of nonlinear programming problems without convexity assumptions. Preliminarily, we introduce a notion of exactness which appears to be of relevance in connection with the solution of the constrained problem by means of unconstrained minimization methods. Then, we show that the class of penalty functions considered is exact, according to this notion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02346160
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  • 2
    Electronic Resource
    Electronic Resource
    A new sequential cluster algorithm for optical lens design (1988)
    Springer
    Journal of optimization theory and applications 59 (1988), S. 165-172 
    Details
    ISSN: 1573-2878
    Keywords: Cluster theory ; artificial intelligence ; decision rules ; optical lens systems ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optical lens design problems are solved by numerical optimization. If we describe an optical lens system by constructive parameters, we may identify such a system by a vectorx ∈ ℝ n . To find an adequate system for a given problem, we have to organize the optimization process in a parameter space with a fixed dimensionn. Often, such an optimization leads to inadequate results. For this reason, we have to alter the number of lenses contained in the system. Consequently, we have to change the dimension of the space for the parametric description of the lens system. This paper describes a special sequential cluster algorithm to realize the move from one parameter space to another by computation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938306
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  • 3
    Electronic Resource
    Electronic Resource
    Numerical experiments with variations of the Gauss-Newton algorithm for nonlinear least squares (1988)
    Springer
    Journal of optimization theory and applications 57 (1988), S. 323-339 
    Details
    ISSN: 1573-2878
    Keywords: Mathematical programming ; nonlinear programming ; nonlinear least squares ; quasi-Newton methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the classical Gauss-Newton method for the unconstrained least squares problem is modified by introducing a quasi-Newton approximation to the second-order term of the Hessian. Various quasi-Newton formulas are considered, and numerical experiments show that most of them are more efficient on large residual problems than the Gauss-Newton method and a general purpose minimization algorithm based upon the BFGS formula. A particular quasi-Newton formula is shown numerically to be superior. Further improvements are obtained by using a line search that exploits the special form of the function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938543
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  • 4
    Electronic Resource
    Electronic Resource
    New results on a class of exact augmented Lagrangians (1988)
    Springer
    Journal of optimization theory and applications 58 (1988), S. 259-282 
    Details
    ISSN: 1573-2878
    Keywords: Optimization ; nonlinear programming ; numerical methods ; computational methods ; augmented Lagrangian functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a new continuously differentiable exact augmented Lagrangian is introduced for the solution of nonlinear programming problems with compact feasible set. The distinguishing features of this augmented Lagrangian are that it is radially unbounded with respect to the multiplier and that it goes to infinity on the boundary of a compact set containing the feasible region. This allows one to establish a complete equivalence between the unconstrained minimization of the augmented Lagrangian on the product space of problem variables and multipliers and the solution of the constrained problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939685
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  • 5
    Electronic Resource
    Electronic Resource
    Sensitivity analysis in posynomial geometric programming (1988)
    Springer
    Journal of optimization theory and applications 57 (1988), S. 85-121 
    Details
    ISSN: 1573-2878
    Keywords: Sensitivity analysis ; geometric programming ; duality ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sensitivity analysis results for general parametric posynomial geometric programs are obtained by utilizing recent results from nonlinear programming. Duality theory of geometric programming is exploited to relate the sensitivity results derived for primal and dual geometric programs. The computational aspects of sensitivity calculations are also considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00939331
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  • 6
    Electronic Resource
    Electronic Resource
    Precision, complexity, and computational schemes of the cubic algorithm (1988)
    Springer
    Journal of optimization theory and applications 57 (1988), S. 223-238 
    Details
    ISSN: 1573-2878
    Keywords: Derivative-free optimization ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The cubic algorithm (Ref. 1) is a nongradient method for the solution of multi-extremal, nonconvex Lipschitzian optimization problems. The precision and complexity of this algorithm are studied, and improved computational schemes are proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00938537
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  • 7
    Electronic Resource
    Electronic Resource
    An interior semi-infinite programming method (1988)
    Springer
    Journal of optimization theory and applications 59 (1988), S. 353-367 
    Details
    ISSN: 1573-2878
    Keywords: Semi-infinite programming ; discretization ; approximation ; nonlinear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, a new method for semi-infinite programming problems with convex constraints is presented. The method generates a sequence of feasible points whose cluster points are solutions of the original problem. No maximization over the index set is required. Some computational results are also presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00940304
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