Infinite (semi-infinite) problems to characterize the optimality of nonlinear optimization problems

Considering a generic nonlinear programming problem (NLPP), this paper provides a family of linear infinite problems (LIPs) or linear semi-infinite problems (LSIPs), and establishes the connection between optimality in the respective NLPP and that in the provided LIPs (LSIPs).

[1]  Gholam Reza Jahanshahloo,et al.  Nonsmooth multiobjective optimization using limiting subdifferentials , 2007 .

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

[3]  M. A. López-Cerdá,et al.  Linear Semi-Infinite Optimization , 1998 .

[4]  C. R. Bector,et al.  Principles of Optimization Theory , 2005 .

[5]  B. Mordukhovich.  Variational analysis and generalized differentiation , 2006 .

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

[7]  Mokhtar S. Bazaraa,et al.  Nonlinear Programming: Theory and Algorithms , 1993 .

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

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

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

[11]  Majid Soleimani-damaneh,et al.  Multiple-objective programs in Banach spaces: Sufficiency for (proper) optimality , 2007 .

[12]  B. Mordukhovich.  Maximum principle in the problem of time optimal response with nonsmooth constraints PMM vol. 40, n≗ 6, 1976, pp. 1014-1023 , 1976 .

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

[14]  R. Tyrrell Rockafellar,et al.  Variational Analysis , 1998, Grundlehren der mathematischen Wissenschaften.

[15]  Gerald M. Leibowitz.  Lectures on Complex Function Algebras , 1970 .

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

[17]  Yu. S. Ledyaev,et al.  Nonsmooth analysis and control theory , 1998 .