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Linearization and Gap Function in Nonsmooth Quasiconvex Optimization Using Incident Subdifferential | ||
Control and Optimization in Applied Mathematics | ||
مقاله 5، دوره 7، شماره 1، فروردین 2022، صفحه 79-92 اصل مقاله (392.33 K) | ||
نوع مقاله: Research Article | ||
شناسه دیجیتال (DOI): 10.30473/coam.2022.63088.1196 | ||
نویسنده | ||
Hamed Soroush* | ||
Department of Mathematics, Payame Noor University (PNU), P.O. Box. 19395-4697, Tehran, Iran. | ||
چکیده | ||
The purpose of this paper is to develop nonsmooth optimization problems (P) in which all emerging functions are assumed to be real-valued quasiconvex functions that are defined on a finite-dimensional Euclidean space. First, we introduce two linear optimization problems with the same optimal value of the considered problem. Then, we introduce a real-valued non-negative gap function for (P), and we provide some conditions which ensure that its null points are the same as the optimal solution of problem (P). The results are based on incident subdifferential, which is an important concept in the analysis of quasiconvex functions. | ||
کلیدواژهها | ||
Quasiconvex optimization؛ Linearization؛ Gap function؛ Incident subdifferential | ||
مراجع | ||
[1] Altangerel L., Bot R.I., Wanka G. (2006). “On gap functions for equilibrium problems via Fenchel duality”, Pacific Journal of Optimization, 2, 667-678.
[2] Altangerel L., Bot R.I., Wanka G. (2007). “On the construction of gap functions for variational inequalities via conjugate duality”, Asia-Pacific Journal of Operational Research, 24, 353-371.
[3] Auslender A. (1976). “Optimisation: Méthods numériques”, Masson, Paris.
[4] Caristi G., Kanzi N., Soleimani-Damaneh M. (2018). “On gap functions for nonsmooth multi objective optimization problems”, Optimization Letters, 12, 273-286.
[5] Chen C.Y., Goh C.J., Yang X.Q. (1998). “The gap function of a convex multi criteria optimization problem”, European Journal of Operational Research, 111, 142-151.
[6] Giorgi G., Guerraggio A., Thierselder J. (2004). “Mathematics of optimization, smooth and nonsmooth cases”. Elsivier.
[7] Hassani Bafrani A., Sadeghieh A. (2018). “Quasi-gap and gap functions for non-smooth multi-objective semi-infinite optimization problems”, Control and Optimization in Applied Mathematics, 3, 1-12.
[8] Hearn DW. (1982). “The gap function of a convex program”, Operations Research Letters, 1, 67-71.
[9] Kanzi N., Sadeghieh A., Caristi G. (2019). “Optimality conditions for semi-infinite programming problems involving generalized convexity”, Optimization Letters, 13, 113-126.
[10] Kanzi N., Shaker Ardekani J., Caristi G. (2018). “Optimality, scalarization and duality in linear vector semi-infinite programming”, Optimization, 67, 523-536.
[11] Kanzi N., Soleymani-damaneh M. (2015). “Slater CQ, optimality and duality for quasi-convex semi-infinite optimization problems”, Journal of Mathematical Analysis and Applications, 434, 638-651.
[12] Lin M.H., Carlsson J.G., Ge D., Tsai J.F. (2013). “A review of piecewise linearization methods”, Mathematical problems in Engineering, 7, 14-25.
[13] López M.A., Vercher E. (1983). “Optimality conditions for nondifferentiable convex semi-infinite Programming”, Mathematical Programming, 27, 307-319.
[14] Penot J.P. (1998). “Are generalized derivatives useful for generalized convex functions? In generalized convexity, generalized monotonicity: Recent results”, J.P. Crouzeix, J. E. Martinez-Legaz, and M. Volle, (eds.), Kluwer, Dordrecht., 3-59.
[15] Penot J.P. (2000). “What is quasiconvex analysis?”, Optimization, 47, 35-110.
[16] Penot J.P., Zälinescu C. (2000). “Elements of quasiconûex subdifferential calculus”, Journal of Convex Analysis, 7, 243-269.
[17] Soleymani-damaneh M. (2008). “Infinite (semi-infinite) problems to characterize the optimality of nonlinear optimization problems”, European Journal of Operational Research, 188, 49-56.
[18] Soroush H. (2021). “Topological subdifferential and its role in nonsmooth optimization with quasi-convex data”, Control and Optimization in Applied Mathematics, 5, 83-91.
[19] Still C., Westerlund T. (2010). “A linear programming based optimization algorithm for solving nonlinear programming problems”, European Journal of Operational Research, 200, 658-670. | ||
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