Generalized Fritz John optimality in nonlinear programming in the presence of equality and inequality constraints

In this paper, we study Fritz John type optimality conditions for constrained nonlinear programming in which equality and inequality constraints are together present. We introduce a generalized Fritz John condition which is necessary and sufficient for a feasible point to be an optimal solution unde...

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Bibliographic Details
Published in:Operational research Vol. 16; no. 2; pp. 349 - 364
Main Authors: Slimani, Hachem, Radjef, Mohammed-Said
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2016
Springer Nature B.V
Subjects:
Business and Management
Computational Intelligence
Constraints
Convex analysis
Feasibility
Inequalities
Inequality
Management Science
Mathematical programming
Nonlinear programming
Operational research
Operations Research
Operations Research/Decision Theory
Optimization
Original Paper
Studies
Equality and inequality constraints
Generalized Fritz John condition
26A51
90C30
90C46
Optimality
90C26
Nonlinear programming
Weak pseudo-invexity
ISSN:1109-2858, 1866-1505
Online Access:Get full text
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Summary:In this paper, we study Fritz John type optimality conditions for constrained nonlinear programming in which equality and inequality constraints are together present. We introduce a generalized Fritz John condition which is necessary and sufficient for a feasible point to be an optimal solution under weak invexity. In particular, by combining the introduced generalized Fritz John condition with the invexity with respect to different functions, we obtain sufficient optimality conditions which extend and generalize various results in the literature, and their importance and usefulness are illustrated on examples .
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ISSN:1109-2858
1866-1505
DOI:10.1007/s12351-015-0206-9