Mohamed Hachimi | Ibnou zohr (original) (raw)

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Papers by Mohamed Hachimi

Journal of Mathematical Analysis and Applications, Jan 1, 2001

New classes of generalized (F, ρ)-convexity are introduced for vector-valued functions. Examples ... more New classes of generalized (F, ρ)-convexity are introduced for vector-valued functions. Examples are given to show their relations with (F, ρ)-pseudoconvex, (F, ρ)-quasiconvex, and strictly (F, ρ)-pseudoconvex vector-valued functions. The sufficient optimality conditions and duality results are obtained for multiobjective programming involving generalized (F, ρ)-convex vector-valued functions.

Journal of Mathematical Analysis and Applications, Jan 1, 2006

Recently, Hachimi and Aghezzaf defined generalized (F,α,ρ,d)(F,α,ρ,d)-type I functions, a new cla... more Recently, Hachimi and Aghezzaf defined generalized (F,α,ρ,d)(F,α,ρ,d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. In this paper, the generalized (F,α,ρ,d)(F,α,ρ,d)-type I functions are extended to nondifferentiable functions. By utilizing the new concepts, we obtain several sufficient optimality conditions and prove mixed type and Mond–Weir type duality results for the nondifferentiable multiobjective programming problem.

In this paper, we develop second-order necessary and sufficient optimality conditions for multiob... more In this paper, we develop second-order necessary and sufficient optimality conditions for multiobjective optimization problems with both equality and inequality constraints. First, we generalize the Lin fundamental theorem (Ref. 1) to second-order tangent sets; then, based on the above generalized theorem, we derive second-order necessary and sufficient conditions for efficiency.

Journal of Infection, Jan 1, 2006

Journal of Mathematical Analysis and Applications, Jan 1, 2004

In this paper, new classes of generalized (F,α,ρ,d)-type I functions are introduced for different... more In this paper, new classes of generalized (F,α,ρ,d)-type I functions are introduced for differentiable multiobjective programming. Based upon these generalized functions, first, we obtain several sufficient optimality conditions for feasible solution to be an efficient or weak efficient solution. Second, we prove weak and strong duality theorems for mixed type duality.

Journal of Global Optimization, Jan 1, 2000

In this paper, we are concerned with the multiobjective programming problem with inequality const... more In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond–Weir and general Mond–Weir type duality under the above generalized type I assumptions.

Journal of Mathematical Analysis and Applications, Jan 1, 2001

New classes of generalized (F, ρ)-convexity are introduced for vector-valued functions. Examples ... more New classes of generalized (F, ρ)-convexity are introduced for vector-valued functions. Examples are given to show their relations with (F, ρ)-pseudoconvex, (F, ρ)-quasiconvex, and strictly (F, ρ)-pseudoconvex vector-valued functions. The sufficient optimality conditions and duality results are obtained for multiobjective programming involving generalized (F, ρ)-convex vector-valued functions.

Journal of Mathematical Analysis and Applications, Jan 1, 2006

Recently, Hachimi and Aghezzaf defined generalized (F,α,ρ,d)(F,α,ρ,d)-type I functions, a new cla... more Recently, Hachimi and Aghezzaf defined generalized (F,α,ρ,d)(F,α,ρ,d)-type I functions, a new class of functions that unifies several concepts of generalized type I functions. In this paper, the generalized (F,α,ρ,d)(F,α,ρ,d)-type I functions are extended to nondifferentiable functions. By utilizing the new concepts, we obtain several sufficient optimality conditions and prove mixed type and Mond–Weir type duality results for the nondifferentiable multiobjective programming problem.

In this paper, we develop second-order necessary and sufficient optimality conditions for multiob... more In this paper, we develop second-order necessary and sufficient optimality conditions for multiobjective optimization problems with both equality and inequality constraints. First, we generalize the Lin fundamental theorem (Ref. 1) to second-order tangent sets; then, based on the above generalized theorem, we derive second-order necessary and sufficient conditions for efficiency.

Journal of Infection, Jan 1, 2006

Journal of Mathematical Analysis and Applications, Jan 1, 2004

In this paper, new classes of generalized (F,α,ρ,d)-type I functions are introduced for different... more In this paper, new classes of generalized (F,α,ρ,d)-type I functions are introduced for differentiable multiobjective programming. Based upon these generalized functions, first, we obtain several sufficient optimality conditions for feasible solution to be an efficient or weak efficient solution. Second, we prove weak and strong duality theorems for mixed type duality.

Journal of Global Optimization, Jan 1, 2000

In this paper, we are concerned with the multiobjective programming problem with inequality const... more In this paper, we are concerned with the multiobjective programming problem with inequality constraints. We introduce new classes of generalized type I vector-valued functions. Duality theorems are proved for Mond–Weir and general Mond–Weir type duality under the above generalized type I assumptions.