Results 21 to 30 of about 66 (53)
On a Nonsmooth Vector Optimization Problem with Generalized Cone Invexity
Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012 By using Clarke’s generalized gradients we consider a nonsmooth vector optimization problem with cone constraints and introduce some generalized cone‐invex functions called K‐α‐generalized invex, K‐α‐nonsmooth invex, and other related functions. Several sufficient optimality conditions and Mond‐Weir type weak and converse duality results are obtained ...
Hehua Jiao, Sanyang Liu, Ferenc Hartung
wiley +1 more source
C-efficiency in nondifferentiable vector optimization
, 2013 We study the minimal solutions in a nondifferentiable multiobjective problem, using a relation induced by a cone C, that is C-efficient and C-weakly efficient solutions.
Arana M, Rufian A., CAMBINI, RICCARDO
core +1 more source
Higher‐Order Generalized Invexity in Control Problems
Journal of Control Science and Engineering, Volume 2011, Issue 1, 2011., 2011 We introduce a higher‐order duality (Mangasarian type and Mond‐Weir type) for the control problem. Under the higher‐order generalized invexity assumptions on the functions that compose the primal problems, higher‐order duality results (weak duality, strong duality, and converse duality) are derived for these pair of problems.
S. K. Padhan, C. Nahak, Onur Toker
wiley +1 more source
Journal of Applied Mathematics, Volume 2011, Issue 1, 2011., 2011 A nondifferentiable multiobjective optimization problem with nonempty set constraints is considered, and the equivalence of weakly efficient solutions, the critical points for the nondifferentiable multiobjective optimization problems, and solutions for vector variational‐like inequalities is established under some suitable conditions. Nonemptiness and
Xin-kun Wu +3 more
wiley +1 more source
On Properties of Geodesic η‐Preinvex Functions
Advances in Operations Research, Volume 2009, Issue 1, 2009., 2009 The present paper deals with the properties of geodesic η‐preinvex functions and their relationships with η‐invex functions and strictly geodesic η‐preinvex functions. The geodesic η‐pre‐pseudo‐invex and geodesic η‐pre‐quasi‐invex functions on the geodesic invex set are introduced and some of their properties are discussed.
I. Ahmad +3 more
wiley +1 more source
Continuous‐Time Multiobjective Optimization Problems via Invexity
Abstract and Applied Analysis, Volume 2007, Issue 1, 2007., 2007 We introduce some concepts of generalized invexity for the continuous‐time multiobjective programming problems, namely, the concepts of Karush‐Kuhn‐Tucker invexity and Karush‐Kuhn‐Tucker pseudoinvexity. Using the concept of Karush‐Kuhn‐Tucker invexity, we study the relationship of the multiobjective problems with some related scalar problems.
Valeriano A. De Oliveira +2 more
wiley +1 more source
Generalized preinvex functions and their properties
International Journal of Stochastic Analysis, Volume 2006, Issue 1, 2006., 2006 We introduce some new classes of preinvex and invex functions, which are called ϕ‐preinvex and ϕ‐invex functions. We study some properties of these classes of ϕ‐preinvex (ϕ‐invex) functions. In particular, we establish the equivalence among the ϕ‐preinvex functions, ϕ‐invex functions, and ϕη‐monotonicity of their differential under some suitable ...
Muhammad Aslam Noor, Khalida Inayat Noor
wiley +1 more source
International Journal of Stochastic Analysis, Volume 2006, Issue 1, 2006., 2006 A class of multiobjective variational control and multiobjective fractional variational control problems is considered, and the duality results are formulated. Under pseudoinvexity assumptions on the functions involved, weak, strong, and converse duality theorems are proved.
C. Nahak
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 8, Page 1253-1276, 2005., 2005 We first define a new class of generalized convex n‐set functions, called (𝔉, b, ϕ, ρ, θ)‐univex functions, and then establish a fairly large number of global parametric sufficient optimality conditions under a variety of generalized (𝔉, b, ϕ, ρ, θ)‐univexity assumptions for a discrete minmax fractional subset programming problem.
G. J. Zalmai
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 6, Page 949-973, 2005., 2005 A fairly large number of global semiparametric sufficient efficiency results are established under various generalized (ℱ, b, φ, ρ, θ)‐univexity assumptions for a multiobjective fractional subset programming problem.
G. J. Zalmai
wiley +1 more source