Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming

Lagrange multipliers theorem and saddle point optimality criteria in mathematical programming

We prove a version of Lagrange multipliers theorem for nonsmooth functionals defined on normed spaces. Applying these results, we extend some results about saddle point optimality criteria in mathematical programming. © 2005 Elsevier Inc. All rights reserved.

Lagrange Multipliers and Optimality

Lagrange multipliers used to be viewed as auxiliary variables introduced in a problem of constrained minimization in order to write first-order optimality conditions formally as a system of equations. Modern applications, with their emphasis on numerical methods and more complicated side conditions than equations, have demanded deeper understanding of the concept and how it fits into a larger t...

Nonsmooth interval-valued optimization and saddle-point optimality criteria

In this article, we focus our attention on a nonsmooth interval-valued optimization problem and establish sufficient optimality conditions for a feasible solution to be a LU optimal solution under the invexity assumption. Appropriate duality theorems for Wolfe and Mond-Weir type duals are presented in order to relate the LU optimal solution of primal and dual programs. Moreover, saddle-point ty...

Dynamic Programming and Lagrange Multipliers.

Saddle Point Criteria and Duality in Multiobjective Programming via an Η-approximation Method

In this paper, Antczak’s -approximation approach is used to prove the equivalence between optima of multiobjective programming problems and the -saddle points of the associated -approximated vector optimisation problems. We introduce an -Lagrange function for a constructed -approximated vector optimisation problem and present some modified -saddle point results. Furthermore, we construct an -ap...