Nonsmooth invexity
- 1 December 1990
- journal article
- research article
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
- Vol. 42 (3) , 437-446
- https://doi.org/10.1017/s0004972700028604
Abstract
The concept of invexity is extended to nondifferentiable functions. Characterisations of nonsmooth invexity are derived as well as results in unconstrained and constrained optimisation and duality. The principal analytic tool is the generalised gradient of Clarke for Lipschitz functions.Keywords
This publication has 14 references indexed in Scilit:
- A geometric approach to nonsmooth optimization with sample applicationsNonlinear Analysis, 1987
- What is invexity?The Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1986
- Duality with generalized convexityThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1986
- Nondifferentiable optimization by smooth approximationsOptimization, 1986
- The essence of invexityJournal of Optimization Theory and Applications, 1985
- On duality with generalized convexityMathematische Operationsforschung und Statistik. Series Optimization, 1984
- Generalized gradients of Lipschitz functionalsAdvances in Mathematics, 1981
- Refinements of necessary optimality conditions in nondifferentiable programming IApplied Mathematics & Optimization, 1979
- On optimality conditions in nondifferentiable programmingMathematical Programming, 1978
- Semismooth and Semiconvex Functions in Constrained OptimizationSIAM Journal on Control and Optimization, 1977