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3638. A novel branch and bound algorithm for solving the linear multiplicative programming problems
Invited abstract in session WD-38: Advances in polynomial optimization and its applications, stream Conic Optimization: Theory, Algorithms, and Applications.
Wednesday, 14:30-16:00Room: 34 (building: 306)
Authors (first author is the speaker)
| 1. | Jinyu Dai
|
Abstract
In this talk, we propose a novel branch and bound algorithm for solving the linear multiplicative programming (LMP) problem. A new quadratic relaxation is proposed. We first show that the Hessian matrix of the multiplication of two linear functions has a decomposition form, given by the difference of two rank-one matrices, resulting in a decomposition each quadratic term of the objective function. And then the minus term is relaxed into a linear one. To find the global optimal solutions, branch and bound method is adopted. Theoretical analysis is provided that guarantees the convergence of our algorithm. Numerical experiments show that the new algorithm runs faster than several typical algorithms for certain types of LMP.
Keywords
- Programming, Quadratic
- Continuous Optimization
- Algorithms
Status: accepted
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