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Papers by Khadija Hamdaoui

In this note, we are concerned with a multiobjective optimization problem with respect to a varia... more In this note, we are concerned with a multiobjective optimization problem with respect to a variable ordering map. Using a special (nonlinear) scalarization [1], together with an exact separation principle recently introduced by Zheng,Yang and Zou [10], we give necessary optimality conditions for locally weakly nondominated solutions with respect to a given ordering map. To get the results, a nonsmooth sequential Guignard constraint qualification is introduced.

Optimization, 2020

In this paper, we investigate a multiobjectif bilevel programming problem with set valued constra... more In this paper, we investigate a multiobjectif bilevel programming problem with set valued constraints in both the upper problem and the lower problem. Using the notion of the support function to the feasible set mapping, together with an appropriate constraint qualification, we establish necessary optimality conditions in terms of asymptotical pointwise compact approximations; continuity of data functions and compactness of approximations are not necessarily required. In order to get sufficient optimality conditions, we introduce generalized pseudo-invexity and quasi-invexity notions in terms of asymptotical pointwise compact approximations. Examples that illustrate our results are given.

Positivity, 2019

In this paper, we have pointed out that the proof of Theorem 11 in the recent paper (Lafhim in Po... more In this paper, we have pointed out that the proof of Theorem 11 in the recent paper (Lafhim in Positivity, 2019.

Optimization Letters, 2019

In this note, we are concerned with an optimization problem (P) where the objective function is t... more In this note, we are concerned with an optimization problem (P) where the objective function is the difference of two quasiconvex functions. Using a suitable subdifferential introduced by Suzuki and Kuroiwa (Nonlinear Anal 74:1279-1285, 2011), we give necessary optimality conditions. An example is given to illustrate the result.

Nonlinear Analysis: Theory, Methods & Applications, 2012

In this paper we study bilevel minimization problems. Using the implicit function theorem, variat... more In this paper we study bilevel minimization problems. Using the implicit function theorem, variational analysis and exact penalty results we establish necessary optimality conditions for these problems.

Journal of Optimization Theory and Applications, 1995

In this paper, we are concerned with a bilevel multiobjective optimization problem (P). Using the... more In this paper, we are concerned with a bilevel multiobjective optimization problem (P). Using the function introduced by Gadhi and Dempe [Necessary optimality conditions and a new approach to multiobjective bilevel optimization problems. J Optim Theory Appl. 2012;155:100-114], we reformulate (P) as a single level mathematical programming problem (P *) and establish/exhibit the global equivalence between the two problems (P) and (P *). Using a generalized convexity introduced by Dutta and Chandra [Convexificator, generalized convexity and vector optimization. Optimization. 2004;53:77-94], we derive sufficient optimality conditions for the problem (P) and establish Mond-Weir duality results. To illustrate the obtained results some examples are given.

$Research paper thumbnail of Necessary optimality conditions for fractional difference problems of the calculus of variations$

Discrete & Continuous Dynamical Systems - A, 2010

We introduce a discrete-time fractional calculus of variations. First and second order necessary ... more We introduce a discrete-time fractional calculus of variations. First and second order necessary optimality conditions are established. Examples illustrating the use of the new Euler-Lagrange and Legendre type conditions are given. They show that the solutions of the fractional problems coincide with the solutions of the corresponding non-fractional variational problems when the order of the discrete derivatives is an integer value.

$Research paper thumbnail of Optimality results for a specific fractional problem$

Journal of Industrial & Management Optimization, 2017

In this paper, one minimizes a fractional function over a compact set. Using an exact separation ... more In this paper, one minimizes a fractional function over a compact set. Using an exact separation theorem, one gives necessary optimality conditions for strict optimal solutions in terms of Frechet subdifferentials. All data are assumed locally Lipschitz.