-optimal solutions in nonconvex semi-infinite programs with support functions.
Kim, Do Sang, Son, Ta Quang (2011)
Fixed Point Theory and Applications [electronic only]
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Kim, Do Sang, Son, Ta Quang (2011)
Fixed Point Theory and Applications [electronic only]
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Nguyen Dinh, Miguel A. Goberna, Marco A. López, Ta Quang Son (2007)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper provides KKT and saddle point optimality conditions, duality theorems and stability theorems for consistent convex optimization problems posed in locally convex topological vector spaces. The feasible sets of these optimization problems are formed by those elements of a given closed convex set which satisfy a (possibly infinite) convex system. Moreover, all the involved functions are assumed to be convex, lower semicontinuous and proper (but not necessarily real-valued)....
Luka Neralić, Sanjo Zlobec (1996)
Applications of Mathematics
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We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction,...