A note on Fritz John sufficiency
نویسنده
چکیده
منابع مشابه
Convex Generalized Semi-Infinite Programming Problems with Constraint Sets: Necessary Conditions
We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...
متن کاملThe Fritz John Necessary Optimality Conditions in the Presence of Equality and Inequality Constraints
Optimality criteria form the foundations of mathematical programming both theoretically and computationally. In general, these criteria can be classified as either necessary or sufficient. Of course, one would like to have the same criterion be both necessary and sufficient. However, this occurs only under somewhat ideal conditions which are rarely satisfied in practice. In the absence of conve...
متن کاملAn elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions in nonlinear programming
In this note we give an elementary proof of the Fritz-John and Karush–Kuhn–Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints. The proof avoids the implicit function theorem usually applied when dealing with equality constraints and uses a generalization of Farkas lemma and the Bolzano-Weierstrass property for compact sets. 2006 P...
متن کاملFritz-John Type Optimality Conditions for Weak Efficient Solutions of Vector Equilibrium Problems with Constraints in Terms of Contingent Epiderivatives∗
In this paper, Fritz-John type optimality conditions for weak efficient solutions in terms of contingent epiderivatives of vector variational inequalities and vector optimization problems with constraints are derived. Under assumptions on quasiconvexity of scalar functions, Fritz-John type necessary optimality conditions become Fritz-John type sufficient optimality conditions. Mathematics Subje...
متن کاملCarathéodory–john-type Sufficiency Criteria in Continuous-time Nonlinear Programming under Generalized (α, Ρ)− (η, Θ)-type I Invexity
Continuous-time linear programming was first introduced by Bellman [1] in the treatment of production and inventory “bottleneck” problems. He formulated the dual problem, established a weak duality theorem and described sufficient optimality conditions. Tyndall [12] extended Bellman’s theory and obtained existence and duality theorems for a class of continuous linear programming problem. Levins...
متن کامل