scholarly journals A range division and contraction approach for nonconvex quadratic program with quadratic constraints

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Chunshan Xue ◽  
Hongwei Jiao ◽  
Jingben Yin ◽  
Yongqiang Chen
Keyword(s):  
Quadratic Program ◽  
Quadratic Constraints ◽  
Nonconvex Quadratic Program

scholarly journals Quadratic Program on a Structured Nonconvex Set

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Yi Xu ◽  
Lili Han
Keyword(s):  
Numerical Results ◽  
New Method ◽  
Convex Program ◽  
Quadratic Program ◽  
Small Scale ◽  
Bilevel Program ◽  
Feasible Set ◽  
Low Level ◽  
Nonconvex Quadratic Program ◽  
Upper Level

In this paper, we focus on a special nonconvex quadratic program whose feasible set is a structured nonconvex set. To find an effective method to solve this nonconvex program, we construct a bilevel program, where the low-level program is a convex program while the upper-level program is a small-scale nonconvex program. Utilizing some properties of the bilevel program, we propose a new algorithm to solve this special quadratic program. Finally, numerical results show that our new method is effective and efficient.

On The Reduction of Duality Gap in Box Constrained Nonconvex Quadratic Program

2011 ◽  
Vol 21 (3) ◽  
pp. 706-729 ◽  
Author(s):  
Yong Xia ◽  
Xiaoling Sun ◽  
Duan Li ◽  
Xiaojin Zheng
Keyword(s):  
Duality Gap ◽  
Quadratic Program ◽  
Nonconvex Quadratic Program

On the Heisenberg Supermagnet Model in (2+1)-Dimensions

2017 ◽  
Vol 72 (4) ◽  
pp. 331-337 ◽  
Author(s):  
Zhao-Wen Yan
Keyword(s):  
Integrable System ◽  
Integrable Systems ◽  
Bäcklund Transformations ◽  
Quadratic Constraints ◽  
Backlund Transformations

AbstractThe Heisenberg supermagnet model is an important supersymmetric integrable system in (1+1)-dimensions. We construct two types of the (2+1)-dimensional integrable Heisenberg supermagnet models with the quadratic constraints and investigate the integrability of the systems. In terms of the gage transformation, we derive their gage equivalent counterparts. Furthermore, we also construct new solutions of the supersymmetric integrable systems by means of the Bäcklund transformations.

scholarly journals On monotonicity and search strategies in face-based copositivity detection algorithms

2021 ◽  
Author(s):  
B. G.-Tóth ◽  
E. M. T. Hendrix ◽  
L. G. Casado
Keyword(s):  
Research Question ◽  
Quadratic Function ◽  
Mixed Integer ◽  
Quadratic Program ◽  
Matrix Methods ◽  
Detection Algorithms ◽  
Standard Simplex ◽  
Mathematical Properties ◽  
The Face ◽  
Spatial Branch And Bound

AbstractOver the last decades, algorithms have been developed for checking copositivity of a matrix. Methods are based on several principles, such as spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration of KKT points or face-based search. Our research question focuses on exploiting the mathematical properties of the relative interior minima of the standard quadratic program (StQP) and monotonicity. We derive several theoretical properties related to convexity and monotonicity of the standard quadratic function over faces of the standard simplex. We illustrate with numerical instances up to 28 dimensions the use of monotonicity in face-based algorithms. The question is what traversal through the face graph of the standard simplex is more appropriate for which matrix instance; top down or bottom up approaches. This depends on the level of the face graph where the minimum of StQP can be found, which is related to the density of the so-called convexity graph.

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