Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction

Atamtürk, Alper; Deck, Carlos; Jeon, Hyemin

doi:10.1287/ijoc.2018.0870

Cited by 2 publications

(2 citation statements)

References 37 publications

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“…On the other hand, if t = 0, then PO reduces to problem min x∈R n {c x : Ax = b, x ≥ 0, x Qx = 0} , which corresponds to CO with x Qx = 0, and hence they are equivalent. Proposition 2 indeed holds for more general problems; it is not necessary to have a polyhedral feasible set [9]. Since they are equivalent optimization problems, we can use PO to solve CO.…”

Section: Formulationmentioning

confidence: 78%

Simplex QP-based methods for minimizing a conic quadratic objective over polyhedra

Atamtürk

Gómez

2018

Math. Prog. Comp.

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We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be solved by polynomial interior point algorithms for conic quadratic optimization. However, interior point algorithms are not well-suited for branch-and-bound algorithms for the discrete counterparts of these problems due to the lack of effective warm starts necessary for the efficient solution of convex relaxations repeatedly at the nodes of the search tree.In order to overcome this shortcoming, we reformulate the problem using the perspective of the quadratic function. The perspective reformulation lends itself to simple coordinate descent and bisection algorithms utilizing the simplex method for quadratic programming, which makes the solution methods amenable to warm starts and suitable for branch-and-bound algorithms. We test the simplex-based quadratic programming algorithms to solve convex as well as discrete instances and compare them with the state-of-the-art approaches. The computational experiments indicate that the proposed algorithms scale much better than interior point algorithms and return higher precision solutions. In our experiments, for large convex instances, they provide up to 22x speed-up. For smaller discrete instances, the speed-up is about 13x over a barrier-based branch-and-bound algorithm and 6x over the LPbased branch-and-bound algorithm with extended formulations.

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Section: Formulationmentioning

confidence: 78%

Simplex QP-based methods for minimizing a conic quadratic objective over polyhedra

Atamtürk

Gómez

2018

Math. Prog. Comp.

Self Cite

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“…For instance, Song and Shen [33] use chance-constrained programming to formulate their risk-averse shortest interdiction path model. Atamtürk et al [34] suggest a convex quadratic mixed-integer program to model the risk-aversion problem of the leader using a mean-risk approach.…”

Section: Literature Reviewmentioning

confidence: 99%

Attack Strategies on Networks With a Budget Constraint

et al. 2021

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In this paper, we develop solutions to the problem of identifying the k most vital cut-sets of a network under limited attacking resources in a network interdiction context. We treat three different versions of the problem, each having a different objective: namely, the highest probability of a successful attack, the least cost attack, and the least expected cost attack combining both success probability and attacking cost. We introduce a budget constraint to reflect the resource limitation of the attacker. We consider both the case of disjoint and non-disjoint cut-sets to target. We develop a simulation-optimization approach accounting for various techniques including the shortest path problem and the min-cut problem. The solution method is found to be very efficient even for large-scale networks. We implement the suggested algorithms for illustration purposes.

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Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction

Cited by 2 publications

References 37 publications

Simplex QP-based methods for minimizing a conic quadratic objective over polyhedra

Simplex QP-based methods for minimizing a conic quadratic objective over polyhedra

Attack Strategies on Networks With a Budget Constraint

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