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Inner approximation algorithm for generalized linear multiplicative programming problems.

Yingfeng Zhao1, Juanjuan Yang1

  • 1School of Mathematical Science, Henan Institute of Science and Technology, Xinxiang, China.

Journal of Inequalities and Applications
|March 7, 2019
PubMed
Summary

An efficient algorithm solves generalized linear multiplicative programming problems by converting them into solvable geometric programming problems. This method demonstrates convergence and practical applications in optimal design.

Keywords:
Generalized multiplicative programmingGeometric programmingInner approximation algorithm

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Area of Science:

  • Optimization
  • Mathematical Programming
  • Operations Research

Background:

  • Generalized linear multiplicative programming (GLMP) problems are complex optimization tasks.
  • Existing methods may struggle with the non-convexity and constraints inherent in GLMP.

Purpose of the Study:

  • To develop an efficient inner approximation algorithm for GLMP with generalized linear multiplicative constraints.
  • To convert GLMP into a series of globally solvable posynomial geometric programming problems.

Main Methods:

  • The proposed algorithm converts the GLMP problem into an equivalent generalized geometric programming problem.
  • Magnifying-shrinking techniques and approximation strategies are employed to transform the problem.
  • The transformed problem is then solved as a series of posynomial geometric programming problems.

Main Results:

  • The algorithm's convergence property is theoretically proven.
  • The effectiveness of the algorithm is validated through practical examples in optimal design.
  • Numerical examples from literature and GLOBALLib confirm the algorithm's performance.

Conclusions:

  • The presented inner approximation algorithm offers an efficient approach to solving GLMP problems.
  • The method is practical for optimal design applications and performs well on benchmark instances.