Decomposition-based interior point methods for stochastic quadratic second-order cone programming

Alzalg, Baha

doi:10.1016/j.amc.2014.10.015

Cited by 12 publications

(7 citation statements)

References 20 publications

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“…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%

“…(28) Because the constraints in the first-stage problem (27) are linear with integer variables and without the use of second-order cone relaxations, a solution for Model (27,28) is now possible. One way to approach this model is by applying scenario-based cuts proposed in [55].…”

Section: Optimal Infrastructure Problem For Electric Vehicles With Battery Swap Technologymentioning

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: )mentioning

confidence: 99%

Section: Optimal Infrastructure Problem For Electric Vehicles With Battery Swap Technologymentioning

confidence: 99%

Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

Alzalg

Alioui

2022

IEEE Access

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“…Note that the constraints in ( [3,4]) are non-positive second-order cone constraints while the common practice in the deterministic second-order cone programming literature is to use non-negative second-order cone constraints. So for convenience we redefine d (k) as d (k) := p k d (k) for k = 1, 2, .…”

Section: Introductionmentioning

confidence: 99%

Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming

Alzalg

2015

Applied Mathematics and Computation

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“…Stochastic second-order cone programming with recourse is a class of optimization problems defined to formulate many applications of DSOCP with uncertain data [2]. Second-order cone programming is a special convex programming model [3], and is one of the important optimization methods in mathematics. The method has been applied in power systems [4,5].…”

Section: Introductionmentioning

confidence: 99%

“…Second-order cone programming is a special convex programming model [3], and is one of the important optimization methods in mathematics. The method has been applied in power systems [4,5].…”

Section: Introductionmentioning

confidence: 99%

Two-stage optimization method for power loss and voltage profile control in distribution systems with DGs and EVs using stochastic second-order cone programming

TANG¹,

Jiekang²,

Wu³

et al. 2018

Turk J Elec Eng & Comp Sci

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This paper introduces a stochastic second-order cone programming (SSCOP) approach to solve the distributed generation coordination problem considering the uncertainty of electric vehicle charging in distribution networks. To minimize the total power loss in the distribution system, the problem is formulated to coordinate the output power of distributed generations (DGs). Two stages are presented to solve the optimization problem: the first stage is to optimize the output power of distributed generators without electric vehicle charging in the distribution system, and the second stage is to optimize the output power of distributed generators according to the stochastic increased load due to the uncertainty of electric vehicle charging. The proposed approach is tested on 69-node and 118-node large-scale distribution systems. The simulated results demonstrate the feasibility and effectiveness of SSCOP.

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Decomposition-based interior point methods for stochastic quadratic second-order cone programming

Cited by 12 publications

References 20 publications

Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

Applications of Stochastic Mixed-Integer Second-Order Cone Optimization

Volumetric barrier decomposition algorithms for stochastic quadratic second-order cone programming

Two-stage optimization method for power loss and voltage profile control in distribution systems with DGs and EVs using stochastic second-order cone programming

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