Sufficient optimality criteria and duality for multiobjective variational control problems with -invexity

Sufficient optimality criteria and duality for multiobjective variational control problems with B-(p,r)-invex functions

“…Hachimi and Aghezzaf [13] obtained several mixed type duality results for multiobjective variational programming problems under the introduced concept of generalized type I functions. Nahak and Nanda [23] obtained sufficient optimality criteria and duality results for multiobjective variational control problems under V -invexity assumptions. In [16], Khazafi et al introduced the classes of (B, ρ)-type I functions and generalized (B, ρ)-type I functions and derived a series of sufficient optimality conditions and mixed type duality results for multiobjective control problems.…”

A necessary and sufficient condition for duality in multiobjective variational problems

“…In addition motivated by Bector and Husain (1992), under invexity Nahak and Nanda (1996) extended the optimality results given by to the multiobjective case. Recently, for multiobjective variational problems, Nahak and Nanda (2007) proposed a sufficient condition for solutions and duality under V-invexity, and Hachimi and Aghezzaf (2006) provided sufficient conditions to obtain duality results under generalized ðF; a; q; dÞ-Type I functions. Optimality results given by Martin (1985) were, on the one hand extended to scalar variational problems by Arana et al (2005) who introduced L-KT-pseudoinvexity and proved that it is a necessary and sufficient condition for all Kuhn-Tucker points to be optimal solutions, and on the other hand generalized to multiobjective mathematical programming by Osuna et al (1998Osuna et al ( , 1999 and Arana et al (2008).…”

Duality for vector variational control problems under generalized KT-invexity

“…In this paper we study the following vector variational control problem: In the last years, there is an extensive literature on optimal control problems, for example Mond and Smart [5], Nahak and Nanda [1,2], Nahak [6], Ahmaf [3], Khazafi, Rueda and Enflo [4]. In [1] Nahak and Nanda established sufficient optimality criteria and duality results of multiobjective variational control problems under V − invexity.…”

“…In [1] Nahak and Nanda established sufficient optimality criteria and duality results of multiobjective variational control problems under V − invexity. In [3] Ahmaf gave sufficiency conditions and duality results under generalized ( , , , ) F α ρ θ − V − convexity assumptions.…”