Nonsmooth multiobjective optimization using limiting subdifferentials

In this study, using the properties of limiting subdifferentials in nonsmooth analysis and regarding a separation theorem, some weak Pareto-optimality (necessary and sufficient) conditions for nonsmooth multiobjective optimization problems are proved.

[1]  Brahim Aghezzaf,et al.  Sufficiency and duality in nondifferentiable multiobjective programming involving generalized type I functions , 2004 .

[2]  K. K. Lai,et al.  Nondifferentiable multiobjective programming under generalized d , 2005, Eur. J. Oper. Res..

[3]  Vaithilingam Jeyakumar,et al.  On generalised convex mathematical programming , 1992, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[4]  Santanu K. Mishra,et al.  Second order symmetric duality in mathematical programming with F-convexity , 2000, Eur. J. Oper. Res..

[5]  Brahim Aghezzaf,et al.  Generalized Invexity and Duality in Multiobjective Programming Problems , 2000, J. Glob. Optim..

[6]  Shashi Kant Mishra.  On Multiple-Objective Optimization with Generalized Univexity , 1998 .

[7]  R. Kaul,et al.  Optimality criteria and duality in multiple-objective optimization involving generalized invexity , 1994 .

[8]  G. Giorgi,et al.  The Notion of Invexity in Vector Optimization: Smooth and Nonsmooth Case , 1998 .

[9]  Kok Lay Teo,et al.  Higher-order generalized convexity and duality in nondifferentiable multiobjective mathematical programming ✩ , 2004 .

[10]  M. A. Hanson,et al.  Optimality criteria in mathematical programming involving generalized invexity , 1988 .

[11]  M. A. Hanson,et al.  Necessary and sufficient conditions in constrained optimization , 1987, Math. Program..

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

[13]  Katta G. Murty,et al.  Nonlinear Programming Theory and Algorithms , 2007, Technometrics.

[14]  M. A. Hanson.  On sufficiency of the Kuhn-Tucker conditions , 1981 .

[15]  Shashi Kant Mishra,et al.  Some nondifferentiable multiobjective programming problems , 2006 .

[16]  Kin Keung Lai,et al.  Optimality and duality for multiple-objective optimization under generalized type I univexity☆ , 2005 .

[17]  Majid Soleimani-Damaneh.  On optimality and duality for multiple-objective optimization under generalized type I univexity , 2009, Int. J. Comput. Math..