Abstract
Optimality conditions are derived for a nonliear program in which a support function appears in the objective as well as in each constraint function. Wolfe and Mond-Weir type duals to this program are presented and various dualityresults are established under suitable convexity and generalized convexity assumptions. Special cases that often occur in the literature are those in which a support function is the square root of a positive semidefinite quadratic form or anLp norm. It is pointed out that these special cases can easily be generated from our results.
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I HUSAIN is professor in the Department of Mathematics at the Regional Engineering College, Srinagar, Kashmir, India. He received his M.A. in Mathematics from Banaras Hindu University, Varanasi, India and Ph.D. in Operations Research from Indian Institute of Technology, Delhi. His major areas of research interest are in Mathematical programming including Continuous-time programming, generalization of convexity and Optimization (optimality criteria, duality, etc.). He is author and co-author of numerous research papers on previous mentioned research field. He has refereed several research aricles. He is a lifemember of Operational Research Society of India.
ABHA has received her M.Sc. in mathematics from the University of Roorkee, Roorkee, India and Ph.D. in Operations Research from Indian Institute of Technology, Delhi, India. She is a lecturer of Mathematics at Indraprastha University, Delhi and her research interests lies in Mathematical Programming.
Z.JABEEN is a lecturer at Regional Engineering College, Srinagar, Kashmir, India. She has obtained her M.Sc. in Statistics from the University of Kashmir, Srinagar and is pursuing a Ph.D. programme in Operations Research.
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Husain, I., Abha & Jabeen, Z. On nonlinear programming with support functions. JAMC 10, 83–99 (2002). https://doi.org/10.1007/BF02936208
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DOI: https://doi.org/10.1007/BF02936208