Convexificators and necessary conditions for efficiency

In this article we establish necessary conditions for local Pareto and weak minima of multiobjective programming problems involving inequality, equality and set constraints in Banach spaces in terms of convexificators.

[1]  Hubert Halkin,et al.  Implicit Functions and Optimization Problems without Continuous Differentiability of the Data , 1974 .

[2]  Joydeep Dutta,et al.  Convexifactors, generalized convexity and vector optimization , 2004 .

[3]  Dinh The Luc A Multiplier Rule for Multiobjective Programming Problems with Continuous Data , 2002, SIAM J. Optim..

[4]  Juha Heinonen,et al.  NONSMOOTH CALCULUS , 2005 .

[5]  Joydeep Dutta,et al.  Convexifactors, Generalized Convexity, and Optimality Conditions , 2002 .

[6]  Bienvenido Jiménez,et al.  On constraint qualifications in directionally differentiable multiobjective optimization problems , 2004, RAIRO Oper. Res..

[7]  T. Maeda Constraint qualifications in multiobjective optimization problems: Differentiable case , 1994 .

[8]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[9]  B. T. Poljak,et al.  Lectures on mathematical theory of extremum problems , 1972 .

[10]  B. Mordukhovich,et al.  On Nonconvex Subdifferential Calculus in Banach Spaces , 1995 .

[11]  Vaithilingam Jeyakumar,et al.  Nonsmooth Calculus, Minimality, and Monotonicity of Convexificators , 1999 .

[13]  Jane J. Ye,et al.  Multiplier Rules Under Mixed Assumptions of Differentiability and Lipschitz Continuity , 2000, SIAM J. Control. Optim..

[14]  On alternative theorems and necessary conditions for efficiency , 2009 .

[15]  V. Jeyakumar,et al.  Approximate Jacobian Matrices for Nonsmooth Continuous Maps and C 1 -Optimization , 1998 .