A Note on Embeddings for the Augmented Lagrange Method
Gemayqzel Bouza-Allende, Jurgen Guddat (2010)
The Yugoslav Journal of Operations Research
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Gemayqzel Bouza-Allende, Jurgen Guddat (2010)
The Yugoslav Journal of Operations Research
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Miroslav Tůma (1991)
Kybernetika
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Ladislav Lukšan (1984)
Kybernetika
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Jürgen Guddat, Francisco Guerra, Dieter Nowack (1998)
The Yugoslav Journal of Operations Research
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Jiří V. Outrata (1999)
Kybernetika
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The paper deals with mathematical programs, where parameter-dependent nonlinear complementarity problems arise as side constraints. Using the generalized differential calculus for nonsmooth and set-valued mappings due to B. Mordukhovich, we compute the so-called coderivative of the map assigning the parameter the (set of) solutions to the respective complementarity problem. This enables, in particular, to derive useful 1st-order necessary optimality conditions, provided the complementarity...
Laureano F. Escudero (1981)
Qüestiió
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We discuss in this work the first-order, second-order and pseudo-second-order estimations of Lagrange multipliers in nonlinear constrained minimization. The paper also justifies estimations and strategies that are used by two nonlinear programming algorithms that are also briefly described.
Ladislav Lukšan (1986)
Aplikace matematiky
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The paper describes the dual method for solving a special problem of quadratic programming as a subproblem at nonlinear minimax approximation. Two cases are analyzed in detail, differring in linear dependence of gradients of the active functions. The complete algorithm of the dual method is presented and its finite step convergence is proved.