Displaying similar documents to “Minimization of a convex quadratic function subject to separable conical constraints in granular dynamics”

Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

Zhisong Hou, Hongwei Jiao, Lei Cai, Chunyang Bai (2017)

Open Mathematics

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This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound...

Quadratic 0–1 programming: Tightening linear or quadratic convex reformulation by use of relaxations

Alain Billionnet, Sourour Elloumi, Marie-Christine Plateau (2008)

RAIRO - Operations Research

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Many combinatorial optimization problems can be formulated as the minimization of a 0–1 quadratic function subject to linear constraints. In this paper, we are interested in the exact solution of this problem through a two-phase general scheme. The first phase consists in reformulating the initial problem either into a compact mixed integer linear program or into a 0–1 quadratic convex program. The second phase simply consists in submitting the reformulated problem to a standard solver....

Modifications of the limited-memory BFGS method based on the idea of conjugate directions

Vlček, Jan, Lukšan, Ladislav

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Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections of the used difference vectors (derived from the idea of conjugate directions), utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. The algorithm is globally convergent for...

On semidefinite bounds for maximization of a non-convex quadratic objective over the unit ball

Mustafa Ç. Pinar, Marc Teboulle (2006)

RAIRO - Operations Research

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We consider the non-convex quadratic maximization problem subject to the unit ball constraint. The nature of the norm structure makes this problem extremely hard to analyze, and as a consequence, the same difficulties are encountered when trying to build suitable approximations for this problem by some tractable convex counterpart formulations. We explore some properties of this problem, derive SDP-like relaxations and raise open questions.