Convex reformulations of Integer Quadratically Constrained Problems

Abstract : We consider a general integer program (QQP) where both the objective function and the constraints are quadratic. We show that the quadratic convex reformulation approach can be extended to that case. This approach consists in designing a program, equivalent to QQP, with a quadratic convex objective function and linear or quadratic convex constraints. The resulting program is then solved by a standard solver. We start by dealing with the objective function. For this, we solve a semi-definite program from which we deduce a reformulation of (QQP) as an equivalent problem (P) having a convex quadratic objective function. We then handle the quadratic constraints of (P). We propose and compare linear and quadratic convex reformulations of these constraints. Finally, we give some numerical results comparing our different approaches.
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Conference papers
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https://hal.archives-ouvertes.fr/hal-01126039
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Submitted on : Friday, March 6, 2015 - 11:37:35 AM
Last modification on : Thursday, February 6, 2020 - 5:33:22 PM

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Alain Billionnet, Sourour Elloumi, Amélie Lambert. Convex reformulations of Integer Quadratically Constrained Problems. ISMP (21th International Symposium of Mathematical programming), Aug 2012, Berlin, Germany. 1 page. ⟨hal-01126039⟩

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