An Infeasible Interior-Point Algorithm for Stochastic Second-Order Cone Optimization

Alzalg, Baha; Badarneh, Khaled; Ababneh, Ayat

doi:10.1007/s10957-018-1445-8

Cited by 3 publications

(5 citation statements)

References 18 publications

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“…In 2015, Alzalg [29] proposed a volumetric barrier decomposition-based interior-point algorithm for solving the problem. In 2018, Alzalg et al [31] proposed an infeasible self-dual interior-point algorithm for solving the problem. While the methodologies in [30] and [31] (…”

Section: A Homogeneous Interior-point Methods For Ssocpmentioning

confidence: 99%

“…In 2018, Alzalg et al [31] proposed an infeasible self-dual interior-point algorithm for solving the problem. While the methodologies in [30] and [31] (…”

Section: A Homogeneous Interior-point Methods For Ssocpmentioning

confidence: 99%

“…for f + 1 ≤ j ≤ f + r, 1 ≤ k ≤ f + r, j k. For example, in Figure 10, it can be seen that vessels V j and V m satisfy the inequality in (31).…”

Section: E Optimal Random Berth Allocation Problem With Uncertain Handling Timementioning

confidence: 99%

“…In this case, the SMISOCP problem (3,4) is reduced to the two-stage SSOCP problem with recourse [20]. SSOCP is a convex optimization problem that can be solved in several methods in polynomial time (see [28]- [31]). In fact, Ax ⪰ k b if and only if the vector Ax − b is nonnegative, i.e., all its components belong to the first-dimensional second-order cone Q 1 := {t ∈ R : t ≥ 0}.…”

Section: )mentioning

confidence: 99%

“…Since this paper mainly introduces SMISOCP from a practical point of view, we do not provide each application model with a specific algorithm to solve it. Nevertheless, a solution method for the generic SMISOCP is presented in this paper to combine existing efficient barrier [27]- [29], homogeneous [30], and infeasible [31] algorithms for SSOCP with extensions of DMISOCP algorithms [32]- [34] (see also [35]- [37]). Related aspects are tackled in an algorithmic companion paper [38].…”

Section: Introductionmentioning

confidence: 99%

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Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

Alzalg

Alioui

2022

IEEE Access

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Second-order cone programming problems are a tractable subclass of convex optimization problems that can be solved using polynomial algorithms. In the last decade, stochastic second-order cone programming problems have been studied, and efficient algorithms for solving them have been developed. The mixed-integer version of these problems is a new class of interest to the optimization community and practitioners, in which certain variables are required to be integers. In this paper, we describe five applications that lead to stochastic mixedinteger second-order cone programming problems. Additionally, we present solution algorithms for solving stochastic mixed-integer second-order cone programming using cuts and relaxations by combining existing algorithms for stochastic second-order cone programming with extensions of mixed-integer second-order cone programming. The applications, which are the focus of this paper, include facility location, portfolio optimization, uncapacitated inventory, battery swapping stations, and berth allocation planning. Considering the fact that mixed-integer programs are usually known to be NP-hard, bringing applications to the surface can detect tractable special cases and inspire for further algorithmic improvements in the future. INDEX TERMSSecond-order cone programming, Mixed-integer programming, Stochastic programming, Applications, Algorithms ACRONYMS CVaR Conditional value-at-risk. DMISOCP Deterministic mixed-integer second-order cone programming. FEU 40-foot equivalent unit. FLP Facility location problem. SMBSOCP Stochastic mixed-binary second-order cone programming. SMILP Stochastic mixed-integer linear programming. SMISOCP Stochastic mixed-integer second-order cone programming. SSOCP Stochastic second-order cone programming. TEU 20-foot equivalent unit.

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Section: A Homogeneous Interior-point Methods For Ssocpmentioning

confidence: 99%

“…In 2018, Alzalg et al [31] proposed an infeasible self-dual interior-point algorithm for solving the problem. While the methodologies in [30] and [31] (…”

Section: A Homogeneous Interior-point Methods For Ssocpmentioning

confidence: 99%

“…for f + 1 ≤ j ≤ f + r, 1 ≤ k ≤ f + r, j k. For example, in Figure 10, it can be seen that vessels V j and V m satisfy the inequality in (31).…”

Section: E Optimal Random Berth Allocation Problem With Uncertain Handling Timementioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

Alzalg

Alioui

2022

IEEE Access

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On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization

Alzalg

Oulha

2022

Positivity

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An Algebraic-Based Primal–Dual Interior-Point Algorithm for Rotated Quadratic Cone Optimization

Tamsaouete

Alzalg

2023

Computation

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In rotated quadratic cone programming problems, we minimize a linear objective function over the intersection of an affine linear manifold with the Cartesian product of rotated quadratic cones. In this paper, we introduce the rotated quadratic cone programming problems as a “self-made” class of optimization problems. Based on our own Euclidean Jordan algebra, we present a glimpse of the duality theory associated with these problems and develop a special-purpose primal–dual interior-point algorithm for solving them. The efficiency of the proposed algorithm is shown by providing some numerical examples.

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An Infeasible Interior-Point Algorithm for Stochastic Second-Order Cone Optimization

Cited by 3 publications

References 18 publications

Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

On approximate solutions for robust semi-infinite multi-objective convex symmetric cone optimization

An Algebraic-Based Primal–Dual Interior-Point Algorithm for Rotated Quadratic Cone Optimization

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