Generalized augmented Lagrangian problem and approximate optimal solutions in nonlinear programming.
Chen, Zhe, Zhao, Kequan, Chen, Yuke (2007)
Journal of Inequalities and Applications [electronic only]
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Displaying similar documents to “Further study on strong Lagrangian duality property for invex programs via penalty functions.”
Generalized augmented Lagrangian problem and approximate optimal solutions in nonlinear programming.
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International Journal of Mathematics and Mathematical Sciences
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Augmented Lagrangian methods for variational inequality problems
Alfredo N. Iusem, Mostafa Nasri (2010)
RAIRO - Operations Research
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We introduce augmented Lagrangian methods for solving finite dimensional variational inequality problems whose feasible sets are defined by convex inequalities, generalizing the proximal augmented Lagrangian method for constrained optimization. At each iteration, primal variables are updated by solving an unconstrained variational inequality problem, and then dual variables are updated through a closed formula. A full convergence analysis is provided, allowing for inexact solution of...
Linear programming interpretations of Mather’s variational principle
L. C. Evans, D. Gomes (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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We discuss some implications of linear programming for Mather theory [13, 14, 15] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an -dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [6, 7, 8, 5].
Monotonicity of the Lagrangian function in the parametric interior point methods of convex programming.
Hamala, M., Halická, M. (1992)
Acta Mathematica Universitatis Comenianae. New Series
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Remarks on second order generalized derivatives for differentiable functions with Lipschitzian Jacobian.
La Torre, Davide, Rocca, Matteo (2003)
Applied Mathematics E-Notes [electronic only]
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Existence of local saddle points for a new augmented Lagrangian function.
Zhao, Wenling, Zhang, Jing, Zhou, Jinchuan (2010)
Mathematical Problems in Engineering
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Asymptotic analysis, existence and sensitivity results for a class of multivalued complementarity problems
Fabián Flores-Bazán, Rubén López (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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In this work we study the multivalued complementarity problem on the non-negative orthant. This is carried out by describing the asymptotic behavior of the sequence of approximate solutions to its multivalued variational inequality formulation. By introducing new classes of multifunctions we provide several existence (possibly allowing unbounded solution set), stability as well as sensitivity results which extend and generalize most of the existing ones in the literature. We also present...
Stability analysis of solutions to an optimal control problem associated with a Goursat-Darboux problem
Dariusz Idczak, Marek Majewski, Stanisław Walczak (2003)
International Journal of Applied Mathematics and Computer Science
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In the present paper, some results concerning the continuous dependence of optimal solutions and optimal values on data for an optimal control problem associated with a Goursat-Darboux problem and an integral cost functional are derived.
On dual vector optimization and shadow prices
Letizia Pellegrini (2004)
RAIRO - Operations Research - Recherche Opérationnelle
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In this paper we present the image space analysis, based on a general separation scheme, with the aim of studying lagrangian duality and shadow prices in Vector Optimization. Two particular kinds of separation are considered; in the linear case, each of them is applied to the study of sensitivity analysis, and it is proved that the derivatives of the perturbation function can be expressed in terms of vector Lagrange multipliers or shadow prices.