On optimality conditions in nonsmooth inequality constrained minimization
- 1 January 1987
- journal article
- research article
- Published by Taylor & Francis in Numerical Functional Analysis and Optimization
- Vol. 9 (5-6) , 535-546
- https://doi.org/10.1080/01630568708816246
Abstract
First order necessary optimality conditions for a minimum of an inequality constrained minimization problem are given in terms of approximate quasidifferentials, without the usual differentiability, convexity or locally Lipschitz assumptions. The main result is obtained with the help of a semi-infinite Gordan type alternative theorem. Sufficient conditions for a minimum are also given with the usual convexity assumption replaced by an invex condition.This publication has 9 references indexed in Scilit:
- Some differentiability properties of quasiconvex functions ℝnPublished by Springer Nature ,2005
- On subgradient duality with strong and weak convex functionsJournal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, 1986
- On sufficiency of the Kuhn-Tucker conditionsJournal of Mathematical Analysis and Applications, 1981
- More on subgradient dualityJournal of Mathematical Analysis and Applications, 1979
- Refinements of necessary optimality conditions in nondifferentiable programming IApplied Mathematics & Optimization, 1979
- On optimality conditions in nondifferentiable programmingMathematical Programming, 1978
- Mathematical Programming and Control TheoryPublished by Springer Nature ,1978
- A New Approach to Lagrange MultipliersMathematics of Operations Research, 1976
- Necessary Conditions for an ExtremumMathematics of Computation, 1972