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A range division and contraction approach for nonconvex quadratic program with quadratic constraints
Chunshan Xue1, Hongwei Jiao2, Jingben Yin2
1School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, 466001 China.
Springerplus
|July 28, 2016
Summary
This study introduces a new method for solving complex optimization problems with quadratic constraints. The approach effectively finds global solutions for nonconvex quadratic programming, proving its convergence and demonstrating practical effectiveness.
Area of Science:
- Optimization Theory
- Mathematical Programming
- Computational Mathematics
Background:
- Nonconvex quadratic programming with quadratic constraints is a challenging problem in optimization.
- Existing methods may struggle with global convergence or efficiency for these complex problems.
Purpose of the Study:
- To develop a novel global optimization algorithm for nonconvex quadratic programming with quadratic constraints.
- To introduce a range division and contraction approach for effective problem solving.
Main Methods:
- Constructing underestimating linear relaxation functions to transform the problem.
- Employing a branch and bound scheme combined with a range contraction strategy.
- Developing a novel global optimization algorithm based on these techniques.
Main Results:
- The proposed algorithm effectively solves nonconvex quadratic programs with quadratic constraints.
- Global convergence of the algorithm is theoretically proven.
- Numerical experiments confirm the effectiveness of the developed approach.
Conclusions:
- The novel range division and contraction approach provides an effective method for global optimization.
- The algorithm demonstrates robust performance in solving challenging quadratic programming problems.
- This work contributes a significant advancement in the field of global optimization for constrained nonconvex problems.
Keywords:
Branch and bound schemeGlobal optimizationNonconvex quadratic program with quadratic constraintsRange contraction approachUnderestimating linear relaxationMore Related Videos
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