Convexifactors, generalized convexity and vector optimization
Authors:
- 1 February 2004
- journal article
- research article
- Published by Taylor & Francis in Optimization
- Vol. 53 (1) , 77-94
Abstract
In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors.Keywords
This publication has 13 references indexed in Scilit:
- An open mapping theorem using unbounded generalized JacobiansNonlinear Analysis, 2002
- Convexifactors, Generalized Convexity, and Optimality ConditionsJournal of Optimization Theory and Applications, 2002
- A Multiplier Rule for Multiobjective Programming Problems with Continuous DataSIAM Journal on Optimization, 2002
- Solution Point Characterizations and Convergence Analysis of a Descent Algorithm for Nonsmooth Continuous Complementarity ProblemsJournal of Optimization Theory and Applications, 2001
- Necessary optimality conditions in nondifferentiable vector optimizationOptimization, 2001
- A Sharp Lagrange Multiplier Rule for Nonsmooth Mathematical Programming Problems Involving Equality ConstraintsSIAM Journal on Optimization, 2000
- Nonsmooth Calculus, Minimality, and Monotonicity of ConvexificatorsJournal of Optimization Theory and Applications, 1999
- Approximate Hessian matrices and second-order optimality conditions for nonlinear programming problems with C1-dataThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1999
- Approximate Jacobian Matrices for Nonsmooth Continuous Maps and C1-OptimizationSIAM Journal on Control and Optimization, 1998
- Generalized Monotonicity of Subdifferentials and Generalized ConvexityJournal of Optimization Theory and Applications, 1997