Abstract
An efficient inner approximation algorithm is presented for solving the generalized linear multiplicative programming problem with generalized linear multiplicative constraints. The problem is firstly converted into an equivalent generalized geometric programming problem, then some magnifying-shrinking skills and approximation strategies are used to convert the equivalent generalized geometric programming problem into a series of posynomial geometric programming problems that can be solved globally. Finally, we prove the convergence property and some practical application examples in optimal design domain, and arithmetic examples taken from recent literatures and GLOBALLib are carried out to validate the performance of the proposed algorithm.
Highlights
In this paper, we focus on the following generalized linear multiplicative programming problem: (GLMP) : ⎧ ⎪⎪⎨min ⎪⎪⎩s.t. φ0(y) = φi(y) = P0 j=1 c0j Pi j=1 cij T0j t=1 (f0jt (y))γ0jt Tij t=1 (fijt (y))γijt
1 Introduction In this paper, we focus on the following generalized linear multiplicative programming problem: (GLMP) :
Many works aimed at globally solving special forms of (GLMP) are presented, for example, global algorithms for signomial geometric programming problems, branch and bound algorithms for multiplicative programming with linear constraints, branch and reduction methods for quadratic programming problems, and sum of ratios problems are all in this category [16,17,18,19,20,21]
Summary
We focus on the following generalized linear multiplicative programming problem:. Zhao and Yang Journal of Inequalities and Applications (2018) 2018:354 constraint functions includes a large class of mathematical programs such as generalized geometric programming, multiplicative programming, sum of linear ratios problems, quadratic programming et al [9,10,11,12]. Many works aimed at globally solving special forms of (GLMP) are presented, for example, global algorithms for signomial geometric programming problems, branch and bound algorithms for multiplicative programming with linear constraints, branch and reduction methods for quadratic programming problems, and sum of ratios problems are all in this category [16,17,18,19,20,21].
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