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Quadratic Convex Reformulations for Integer and Mixed-Integer Quadratic Programs
Profiles in Operations Research, 2017We review recent advances in the quadratic convex reformulation (QCR) approach that is employed to derive efficient equivalent reformulations for mixed-integer quadratically constrained quadratic programming (MIQCQP) problems. Although MIQCQP problems can be directly plugged into and solved by standard MIQP solvers that are based on branch-and-bound ...
Rujun Jiang, Baiyi Wu
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Quadratic convex reformulation for graph partitionning problems [PDF]
, 2013 Many graph partitionning problems can be formulated by quadratic programs (QP) with binary variables and linear and quadratic constraints. We apply the general approach that consists in first reformulating the initial (QP) into an equivalent program (QP ).
Elloumi, Sourour, Lambert, Amélie
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Quadratic convex reformulations for a class of complex quadratic programming problems
Computational Optimization and ApplicationszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhibin Deng
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Convex reformulations for binary quadratic programs [PDF]
, 2009 -Let (QP) be a binary quadratic program that consists in minimizing a quadratic function subject to linear constraints. To solve (QP) we reformulate it into an equivalent program with a convex objective function. Our reformulation, that we call EQCR (Extended Quadratic Convex Reformulation), is optimal from the continuous relaxation bound point of view.
Billionnet, Alain +2 more
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Optimization Letters, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cheng Lu 0007, Xiaoling Guo
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cheng Lu 0007, Xiaoling Guo
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Global solution of mixed-integer quadratic programs through quadratic convex reformulation [PDF]
, 2013 We review the quadratic convex reformulation approach for quadratic programs with integer variables. We also show the recent extensions to quadratically constrained programs and to the case of mixed-integer variables. In all these extensions, the global framework is the same: in a preprocessing step, we compute a tight equivalent reformulation of the ...
Elloumi, Sourour +2 more
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Convex reformulations for integer quadratic programs [PDF]
, 2009 -Let (QP) be an integer quadratic program that consists in minimizing a quadratic functionsubject to linear constraints. To solve (QP), we reformulate it into an equivalent program with a convex objective function, and we use a Mixed Integer Quadratic Programming solver. This reformulation, called IQCR, is optimal in a certain sense from the continuous
Billionnet, Alain +2 more
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Quadratic Convex Reformulation for discrete quadratic optimization : Basic results and recent extensions [PDF]
, 2014 We consider problem (QP) of minimizing a quadratic function subject to linear or quadratic constraints. Variables are integer and bounded. This very general problem can model many classical problems in Combinatorial Optimization.A major difference between (QP) and integer linear programs lies in the fact that, in general, its continuous relaxation is ...
Elloumi, Sourour
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Convex reformulations of Integer Quadratically Constrained Problems [PDF]
, 2012 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 ...
Billionnet, Alain +2 more
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A unified view of linear and quadratic convex reformulations for binary quadratic programming [PDF]
, 2012 We consider binary quadratic programs (QP) having a quadratic objectivefunction, linear constraints, and binary variables. Many classical solution methods ofthese problems are based on exact reformulation of QP into anequivalent mixed integer linear program. Several linearization methods werestudied in the literature.
Elloumi, Sourour
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