On First-Order Conditions for Optimality of Nondifferentiable Semi-infinite Programming

Iranian Journal of Science and Technology, Transactions A: Science - Tập 43 - Trang 1643-1647 - 2018
Ali Sadeghieh1
1Department of Mathematics, Islamic Azad University, Yazd, Iran

Tóm tắt

The purpose of this paper is to give some new Karush–Kuhn–Tucker-type necessary optimality conditions for nonsmooth semi-infinite problems. Moreover, we present some suitable examples for our results. The paper is organized by Fréchet and Mordukhovich subdifferentials.

Tài liệu tham khảo

Clarke FM (1983) Optimization and nonsmooth analysis. Wiley, Hoboken

Deepmala (2014) A study on fixed point theorems for nonlinear contractions and its applications. Ph.D. Thesis, Pt. Ravishankar Shukla University, Raipur

Deepmala Mishra VN, Marasi HR, Shabanian H, Nosraty M (2017) Solution of Voltra-Fredholm Integro-Differential equations using Chebyshev collocation method. Global J Technol Optim 8:210. https://doi.org/10.4172/2229-8711.1000210

Fajardo MD, López MA (1999) Locally Farkas-Minkowski systems in convex semi-infinite programming. J Optim Theory Appl 103:313–335

Goberna MA, López MA (1998) Linear semi-infinite optimization. Wiley, Hoboken

Golestani M, Kanzi N (2017) Necessary and sufficient conditions for optimality of nonsmooth semi-infinite programming. Iran J Sci Technol Trans Sci 41:923–929

Hettich R, Kortanek O (1993) Semi-infinite programming: theory, methods, and applications. SIAM Rev 35:380–429

Hiriart-Urruty HB, Lemarechal C (1991) Convex analysis and minimization algorithms. I & II. Springer, Berlin

Kanzi N (2011) Necessary optimality conditions for nonsmooth semi-infinite programming Problems. J Global Optim 49:713–725

Kanzi N (2014) Constraint qualifications in semi-infinite systems and their applications in nonsmooth semi-infinite problems with mixed constraints. SIAM J Optim 24:559–572

Kanzi N (2014) Two constraint qualifications for non-differentiable semi-infinite programming problems using Fréchet and Mordukhovich subdifferentials. J Math Ext 8:83–94

Kanzi N (2015) On strong KKT optimality conditions for multiobjective semi-infinite programming problems with lipschitzian data. Optim Lett 9:1121–1129

Kanzi N, Nobakhtian S (2008) Optimality conditions for nonsmooth semi-infinite programming. Optimization 59:717–727

Kanzi N, Nobakhtian S (2009) Nonsmooth semi-infinite programming problems with mixed constraints. J Math Anal Appl 351:170–181

Li W, Nahak C, Singer I (2000) Constraint qualifications in semi-infinite system of convex inequalities. SIAM J Optim 11:31–52

López MA, Still G (2007) Semi-infinite programming. Eur J Oper Res 180:491–518

López MA, Vercher E (1983) Optimality conditions for nondifferentiable convex semi-infinite Programming. Math Program 27:307–319

Mishra LN (2017) On existence and behavior of solutions to some nonlinear integral equations with applications. Ph.D. Thesis, National Institute of Technology, Silchar

Mishra VN (2007) Some problems on approximations of functions in banach spaces. Ph.D. Thesis, Indian Institute of Technology, Roorkee

Mishra SK, Jaiswal M, LeThi HA (2012) Nonsmooth semi-infinite programming problem using limiting subdifferentials. J Global Optim 53:285–296

Mordukhovich BS (2006) Variational analysis and generalized differentiation. I. Basic theory. Springer, Berlin

Rockafellar RK, Wets JB (1998) Variational analysis. Springer, Berlin

Vandana (2017) A study of dynamic inventory involving economic ordering of commodity. Ph.D. thesis, Pt. Ravishankar Shukla University Raipur, Chhattisgarh

Vandana, Dubey R, Deepmala, Mishra LN, Mishra VN (2018) Duality relations for a class of a multiobjective fractional programming problem involving support functions. Am J Oper Res (in press)

Thông tin
: []
Thông tin xuất bản

Iranian Journal of Science and Technology, Transactions A: Science

Tập 43

1643-1647

Thông tin tác giả