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<p>To solve a minimization linear multiplicative problem (MLMP), we design an adaptive optimization algorithm (AOA) based on the branch-and-bound (B&amp;B) framework. Firstly, a new problem (P) with the same solutions as the problem (MLMP) is constructed. In order to solve the problem (P) globally, some partition variables are introduced to obtain its equivalence problem (EP). And then, the linear optimization problem (LOP) of the problem (EP) is obtained by using a relaxation strategy. Meanwhile, by utilizing the characteristics of some solutions to the problem (LOP), its enhanced linear optimization problem (ELOP) is obtained. Next, an adaptive optimization algorithm (AOA) is designed to globally solve this problem (P), and its theoretical analysis is provided in terms of convergence and complexity. Finally, the effectiveness of the algorithm is illustrated by carrying out some numerical experiments.</p>

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An adaptive optimization algorithm to solve a class of linear multiplicative problems

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • Binbin Li,
  • Yuelin Gao

摘要

To solve a minimization linear multiplicative problem (MLMP), we design an adaptive optimization algorithm (AOA) based on the branch-and-bound (B&B) framework. Firstly, a new problem (P) with the same solutions as the problem (MLMP) is constructed. In order to solve the problem (P) globally, some partition variables are introduced to obtain its equivalence problem (EP). And then, the linear optimization problem (LOP) of the problem (EP) is obtained by using a relaxation strategy. Meanwhile, by utilizing the characteristics of some solutions to the problem (LOP), its enhanced linear optimization problem (ELOP) is obtained. Next, an adaptive optimization algorithm (AOA) is designed to globally solve this problem (P), and its theoretical analysis is provided in terms of convergence and complexity. Finally, the effectiveness of the algorithm is illustrated by carrying out some numerical experiments.