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An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

Yingfeng Zhao1, Sanyang Liu2

  • 1School of Mathematics and Statistics, Xidian University, Xi'an, 710071 China ; School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang, 453003 China.

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Summary
This summary is machine-generated.

A new branch and bound algorithm efficiently solves generalized linear multiplicative programming problems. This method uses a two-phase relaxation technique to find global solutions, proving effective for complex optimization tasks.

Keywords:
Branch and boundGeneralized linear multiplicative programmingGlobal optimization

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Area of Science:

  • Optimization
  • Mathematical Programming
  • Operations Research

Background:

  • Generalized linear multiplicative programming problems present significant computational challenges.
  • Existing methods may struggle with global optimality and efficiency for problems with multiplicative constraints.

Purpose of the Study:

  • To develop a practical algorithm for globally solving generalized linear multiplicative programming problems.
  • To address the complexities introduced by multiplicative constraints.

Main Methods:

  • A novel two-phase relaxation technique is employed to transform the problem into a solvable linear programming problem.
  • A branch and bound framework is utilized to systematically explore the solution space.
  • Lower and upper bounds are derived concurrently through linear relaxation subproblems.

Main Results:

  • The proposed algorithm achieves global convergence.
  • Demonstrated feasibility and efficiency through sample examples and random experiments.
  • The relaxation technique effectively simplifies the complex problem structure.

Conclusions:

  • The presented branch and bound algorithm offers an efficient and feasible approach for global optimization of generalized linear multiplicative programming.
  • The two-phase relaxation technique is a key innovation enabling the solution of these complex problems.