Browsing by Author "Alzalg, Baha"

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    A hybrid branch-and-bound and interior-point algorithm for stochastic mixed-integer nonlinear second-order cone programming
    (Azarbaijan Shahid Madani University, 2025) Alioui, Hadjer; Alzalg, Baha
    One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, IEEE Access, 10:3522-3547, 2022). The linear and nonlinear versions of this class of optimization problems are still unsolved yet. In this paper, we develop a hybrid optimization algorithm coupling branch-and-bound and primal-dual interior-point methods for solving two-stage stochastic mixed-integer nonlinear second-order cone programming. The adopted approach uses a branch-and-bound technique to handle the integer variables and an infeasible interior-point method to solve continuous relaxations of the resulting subproblems. The proposed hybrid algorithm is also implemented to data to show its efficiency
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    Algebraic-based primal interior-point algorithms for stochastic infinity norm optimization
    (Azarbaijan Shahid Madani University, 2024) Alzalg, Baha; Tamsaouete, Karima
    We study the two-stage stochastic infinity norm optimization problem with recourse based on the Jordan algebra. First, we explore and develop the Jordan algebra structure of the infinity norm cone, and utilize it to compute the derivatives of the barrier recourse functions. Then, we prove that the barrier recourse functions and the composite barrier functions for this optimization problem are self-concordant families with reference to barrier parameters. These findings are used to develop interior-point algorithms based on primal decomposition for this class of stochastic programming problems. Our complexity results for the short- and long-step algorithms show that the dominant complexity terms are linear in the rank of the underlying cone. Despite the asymmetry of the infinity norm cone, we also show that the obtained complexity results match (in terms of rank) the best known results in the literature for other well-studied stochastic symmetric cone programs. Finally, we demonstrate the efficiency of the proposed algorithm by presenting some numerical experiments on both stochastic uniform facility location problems and randomly-generated problems.