ASYMPTOTIC CONDITIONS FOR CONSTRAINED MINIMIZATION.
RESEARCH ANALYSIS CORP MCLEAN VA
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The characterization of a local solution of a constrained minimization problem has traditionally been given in terms of the problem functions and the associated Lagrangian evaluated at the solution point for a corresponding set of finite Lagrange multipliers. A recent exception is given by Kortanek and Evans who give a characterization of optimality in terms of limiting properties of the problem functions and associated Lagrangian, taken over an appropriate sequence of points and multipliers. This characterization is significantly generalized, and very general necessary and sufficient asymptotic conditions under various assumptions are obtained. These results enlarge the class of problems for which optimality criteria can be given. In particular, several well-known sets of finite multiplier necessary conditions are implied as special cases, and first- and second-order results such as those obtained by Fritz John, L. Pennisi, and others are extended. Author
- Operations Research