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  • Artikel  (57)
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  • 1
    Digitale Medien
    Digitale Medien
    A continuation method for monotone variational inequalities (1995)
    Springer
    Mathematical programming 69 (1995), S. 237-253 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Variational inequality ; Nonlinear complementarity ; Nonlinear programming ; Continuation method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper presents a continuation method for monotone variational inequality problems based on a new smooth equation formulation. The existence, uniqueness and limiting behavior of the path generated by the method are analyzed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585559
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  • 2
    Digitale Medien
    Digitale Medien
    Pseudopower expansion of solutions of generalized equations and constrained optimization problems (1995)
    Springer
    Mathematical programming 70 (1995), S. 123-148 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Generalized equations ; Variational inequalities ; Nonlinear programming ; Sensitivity analysis ; Power series ; Strong regularity ; Constrained optimization ; Perturbation theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We show that the solution of a strongly regular generalized equation subject to a scalar perturbation expands in pseudopower series in terms of the perturbation parameter, i.e., the expansion of orderk is the solution of generalized equations expanded to orderk and thus depends itself on the perturbation parameter. In the polyhedral case, this expansion reduces to a usual Taylor expansion. These results are applied to the problem of regular perturbation in constrained optimization. We show that, if the strong regularity condition is satisfied, the property of quadratic growth holds and, at least locally, the solutions of the optimization problem and of the associated optimality system coincide. If, in addition the number of inequality constraints is finite, the solution and the Lagrange multiplier can be expanded in Taylor series. If the data are analytic, the solution and the multiplier are analytic functions of the perturbation parameter.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585932
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  • 3
    Digitale Medien
    Digitale Medien
    A trust-region strategy for minimization on arbitrary domains (1995)
    Springer
    Mathematical programming 68 (1995), S. 267-301 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear programming ; Trust-region methods ; Global convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We present a trust-region method for minimizing a general differentiable function restricted to an arbitrary closed set. We prove a global convergence theorem. The trust-region method defines difficult subproblems that are solvable in some particular cases. We analyze in detail the case where the domain is a Euclidean ball. For this case we present numerical experiments where we consider different Hessian approximations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585768
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  • 4
    Digitale Medien
    Digitale Medien
    Proximal level bundle methods for convex nondifferentiable optimization, saddle-point problems and variational inequalities (1995)
    Springer
    Mathematical programming 69 (1995), S. 89-109 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nondifferentiable (nonsmooth) optimization ; Convex programming ; Mathematical programming ; Nonlinear programming ; Saddle-points ; Variational inequalities ; Bundle methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We study proximal level methods for convex optimization that use projections onto successive approximations of level sets of the objective corresponding to estimates of the optimal value. We show that they enjoy almost optimal efficiency estimates. We give extensions for solving convex constrained problems, convex-concave saddle-point problems and variational inequalities with monotone operators. We present several variants, establish their efficiency estimates, and discuss possible implementations. In particular, our methods require bounded storage in contrast to the original level methods of Lemaréchal, Nemirovskii and Nesterov.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585554
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  • 5
    Digitale Medien
    Digitale Medien
    A unifying geometric solution framework and complexity analysis for variational inequalities (1995)
    Springer
    Mathematical programming 71 (1995), S. 327-351 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Variational inequalities ; Nonlinear programming ; Complexity analysis ; Monotone operators
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper, we propose a concept of polynomiality for variational inequality problems and show how to find a near optimal solution of variational inequality problems in a polynomial number of iterations. To establish this result, we build upon insights from several algorithms for linear and nonlinear programs (the ellipsoid algorithm, the method of centers of gravity, the method of inscribed ellipsoids, and Vaidya's algorithm) to develop a unifying geometric framework for solving variational inequality problems. The analysis rests upon the assumption of strong-f-monotonicity, which is weaker than strict and strong monotonicity. Since linear programs satisfy this assumption, the general framework applies to linear programs.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01590959
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  • 6
    Digitale Medien
    Digitale Medien
    An SQP method for general nonlinear programs using only equality constrained subproblems (1998)
    Springer
    Mathematical programming 82 (1998), S. 413-448 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Sequential quadratic programming ; SQP method ; Nonlinear programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we describe a new version of a sequential equality constrained quadratic programming method for general nonlinear programs with mixed equality and inequality constraints. Compared with an older version [P. Spellucci, Han's method without solving QP, in: A. Auslender, W. Oettli, J. Stoer (Eds), Optimization and Optimal Control, Lecture Notes in Control and Information Sciences, vol. 30, Springer, Berlin, 1981, pp. 123–141.] it is much simpler to implement and allows any kind of changes of the working set in every step. Our method relies on a strong regularity condition. As far as it is applicable the new approach is superior to conventional SQP-methods, as demonstrated by extensive numcrical tests. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580078
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  • 7
    Digitale Medien
    Digitale Medien
    NLPQL: A fortran subroutine solving constrained nonlinear programming problems (1986)
    Springer
    Annals of operations research 5 (1986), S. 485-500 
    Details
    ISSN: 1572-9338
    Schlagwort(e): Nonlinear programming ; sequential quadratic programming method ; numerical implementation ; test results
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract NLPQL is a FORTRAN implementation of a sequential quadratic programming method for solving nonlinearly constrained optimization problems with differentiable objective and constraint functions. At each iteration, the search direction is the solution of a quadratic programming subproblem. This paper discusses the organization of NLPQL, including the formulation of the subproblem and the information that must be provided by a user. A summary is given of the performance of different algorithmic options of NLPQL on a collection of test problems (115 hand-selected or application problems, 320 randomly generated problems). The performance of NLPQL is compared with that of some other available codes.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02022087
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  • 8
    Digitale Medien
    Digitale Medien
    Integrating modeling, algorithm design, and computational implementation to solve a large-scale non-linear mixed integer programming problem (1986)
    Springer
    Annals of operations research 5 (1986), S. 395-411 
    Details
    ISSN: 1572-9338
    Schlagwort(e): Nonlinear programming ; decomposition ; branch and bound ; network ; transportation ; mixed integer programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract This paper describes the formulation of a nonlinear mixed integer programming model for a large-scale product development and distribution problem and the design and computational implementation of a special purpose algorithm to solve the model. The results described demonstrate that integrating the art of modeling with the sciences of solution methodology and computer implementation provides a powerful approach for attacking difficult problems. The efforts described here were successful because they capitalized on the wealth of existing modeling technology and algorithm technology, the availability of efficient and reliable optimization, matrix generation and graphics software, and the speed of large-scale computer hardware. The model permitted the combined use of decomposition, general linear programming and network optimization within a branch and bound algorithm to overcome mathematical complexity. The computer system reliably found solutions with considerably better objective function values 30 to 50 times faster than had been achieved using general purpose optimization software alone. Throughout twenty months of daily use, the system was credited with providing insights and suggesting strategies that led to very large dollar savings.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02022082
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  • 9
    Digitale Medien
    Digitale Medien
    A successive quadratic programming algorithm with global and superlinear convergence properties (1986)
    Springer
    Mathematical programming 35 (1986), S. 253-264 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear programming ; successive quadratic programming ; Maratos effect ; exact penalty function ; superlinear convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper presents a successive quadratic programming algorithm for solving general nonlinear programming problems. In order to avoid the Maratos effect, direction-finding subproblems are derived by modifying the second-order approximations to both objective and constraint functions of the problem. We prove that the algorithm possesses global and superlinear convergence properties.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01580879
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  • 10
    Digitale Medien
    Digitale Medien
    Nonlinear programming and nonsmooth optimization by successive linear programming (1989)
    Springer
    Mathematical programming 43 (1989), S. 235-256 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Nonlinear programming ; nonsmooth optimization ; global convergence ; superlinear convergence ; trust region method ; Coleman-Conn method
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Methods are considered for solving nonlinear programming problems using an exactl 1 penalty function. LP-like subproblems incorporating a trust region constraint are solved successively both to estimate the active set and to provide a foundation for proving global convergence. In one particular method, second order information is represented by approximating the reduced Hessian matrix, and Coleman-Conn steps are taken. A criterion for accepting these steps is given which enables the superlinear convergence properties of the Coleman-Conn method to be retained whilst preserving global convergence and avoiding the Maratos effect. The methods generalize to solve a wide range of composite nonsmooth optimization problems and the theory is presented in this general setting. A range of numerical experiments on small test problems is described.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01582292
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