scholarly journals A Novel Optimization Method for Nonconvex Quadratically Constrained Quadratic Programs

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Hongwei Jiao ◽  
Yong-Qiang Chen ◽  
Wei-Xin Cheng
Keyword(s):  
Branch And Bound ◽  
Computational Efficiency ◽  
Numerical Experiments ◽  
Optimization Method ◽  
Global Optimum ◽  
Branch And Bound Algorithm ◽  
Linear Programs ◽  
Quadratic Programs ◽  
Optimum Point ◽  
Quadratically Constrained

This paper presents a novel optimization method for effectively solving nonconvex quadratically constrained quadratic programs (NQCQP) problem. By applying a novel parametric linearizing approach, the initial NQCQP problem and its subproblems can be transformed into a sequence of parametric linear programs relaxation problems. To enhance the computational efficiency of the presented algorithm, a cutting down approach is combined in the branch and bound algorithm. By computing a series of parametric linear programs problems, the presented algorithm converges to the global optimum point of the NQCQP problem. At last, numerical experiments demonstrate the performance and computational superiority of the presented algorithm.

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

2017 ◽  
Vol 15 (1) ◽  
pp. 1212-1224 ◽  
Author(s):  
Zhisong Hou ◽  
Hongwei Jiao ◽  
Lei Cai ◽  
Chunyang Bai
Keyword(s):  
Branch And Bound ◽  
Computational Efficiency ◽  
Global Minimum ◽  
Quadratic Function ◽  
Numerical Results ◽  
Linear Programs ◽  
Quadratic Programs ◽  
New Variables ◽  
Quadratically Constrained ◽  
Methods Numerical

Abstract 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 framework without introducing any new variables and constrained functions, which can be easily solved by any effective linear programs algorithms. By subsequently solving a series of linear relaxed programs problems, the proposed algorithm can converge the global minimum of the initial quadratically constrained quadratic programs problem. Compared with the known methods, numerical results demonstrate that the proposed method has higher computational efficiency.

scholarly journals A parametric linearizing approach for quadratically inequality constrained quadratic programs

2018 ◽  
Vol 16 (1) ◽  
pp. 407-419 ◽  
Author(s):  
Hongwei Jiao ◽  
Rongjiang Chen
Keyword(s):  
Computational Efficiency ◽  
Numerical Results ◽  
Initial Problem ◽  
Linear Programs ◽  
Quadratic Programs ◽  
Relaxation Problem ◽  
Computational Speed ◽  
Global Optima

AbstractIn 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 problem. To accelerate the computational speed of the proposed algorithm, an interval deleting rule is used to reduce the investigated box. The proposed algorithm is convergent to the global optima of the initial problem by subsequently partitioning the initial box and solving a sequence of parametric linear programs relaxation problems. Finally, compared with some existing algorithms, numerical results show higher computational efficiency of the proposed algorithm.

scholarly journals Linear programs with an additional separable concave constraint

2004 ◽  
Vol 8 (3) ◽  
pp. 155-174 ◽  
Author(s):  
Takahito Kuno ◽  
Jianming Shi
Keyword(s):  
Local Search ◽  
Branch And Bound ◽  
Special Class ◽  
Concave Function ◽  
Concave Minimization ◽  
Simplex Algorithm ◽  
Direct Application ◽  
Special Structure ◽  
Branch And Bound Algorithm ◽  
Linear Programs

In this paper, we develop two algorithms for globally optimizing a special class of linear programs with an additional concave constraint. We assume that the concave constraint is defined by a separable concave function. Exploiting this special structure, we apply Falk-Soland's branch-and-bound algorithm for concave minimization in both direct and indirect manners. In the direct application, we solve the problem alternating local search and branch-and-bound. In the indirect application, we carry out the bounding operation using a parametric right-hand-side simplex algorithm.

scholarly journals A Branch-and-Bound Algorithm for Polymatrix Games ϵ-Proper Nash Equilibria Computation

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 365
Author(s):  
Slim Belhaiza
Keyword(s):  
Branch And Bound ◽  
Nash Equilibria ◽  
Decision Makers ◽  
Experimental Results ◽  
Branch And Bound Algorithm ◽  
Linear Programs ◽  
Polymatrix Games

When several Nash equilibria exist in the game, decision-makers need to refine their choices based on some refinement concepts. To this aim, the notion of a ϵ-proper equilibria set for polymatrix games is used to develop 0–1 mixed linear programs and compute ϵ-proper Nash equilibria. A Branch-and-Bound exact arithmetics algorithm is proposed. Experimental results are provided on polymatrix games randomly generated with different sizes and densities.

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