EURO Journal on Computational Optimization, 2021 A conic optimization problem is a problem involving a constraint that the optimization variable be in some closed convex cone. Prominent examples are linear programs (LP), second order cone programs (SOCP), semidefinite problems (SDP), and copositive ...
Mirjam Dür, Franz Rendl
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A fast branch-and-bound algorithm for non-convex quadratic integer optimization subject to linear constraints using ellipsoidal relaxations [PDF]
, 2015 We propose two exact approaches for non-convex quadratic integer minimization subject to linear constraints where lower bounds are computed by considering ellipsoidal relaxations of the feasible set.
Buchheim, Christoph +2 more
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Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs
Open Mathematics, 2017 This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex.
Hou Zhisong +3 more
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On global optimization with indefinite quadratics
EURO Journal on Computational Optimization, 2017 We present an algorithmic framework for global optimization problems in which the non-convexity is manifested as an indefinite-quadratic as part of the objective function.
Marcia Fampa, Jon Lee, Wendel Melo
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Solving Quadratic Programs to High Precision using Scaled Iterative Refinement [PDF]
, 2018 Quadratic optimization problems (QPs) are ubiquitous, and solution algorithms have matured to a reliable technology. However, the precision of solutions is usually limited due to the underlying floating-point operations.
Gleixner, Ambros +2 more
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Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections [PDF]
, 2015 This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems.
Bellavia, S. +3 more
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A parametric linearizing approach for quadratically inequality constrained quadratic programs
Open Mathematics, 2018 In this paper we propose a new parametric linearizing approach for globally solving quadratically inequality constrained quadratic programs. By utilizing this approach, we can derive the parametric linear programs relaxation problem of the investigated ...
Jiao Hongwei, Chen Rongjiang
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Open Mathematics, 2018 In this paper, we present an effective algorithm for globally solving quadratic programs with quadratic constraints, which has wide application in engineering design, engineering optimization, route optimization, etc.
Tang Shuai, Chen Yuzhen, Guo Yunrui
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S-Lemma with Equality and Its Applications [PDF]
, 2015 Let $f(x)=x^TAx+2a^Tx+c$ and $h(x)=x^TBx+2b^Tx+d$ be two quadratic functions having symmetric matrices $A$ and $B$. The S-lemma with equality asks when the unsolvability of the system $f(x)
R. L. Sheu +6 more
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A two-phase gradient method for quadratic programming problems with a single linear constraint and bounds on the variables [PDF]
, 2018 We propose a gradient-based method for quadratic programming problems with a single linear constraint and bounds on the variables. Inspired by the GPCG algorithm for bound-constrained convex quadratic programming [J.J. Mor\'e and G.
Barlow, Jesse +3 more
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