Range division and linearization algorithm for a class of linear ratios optimization problems

Shen, Peiping; Huang, Bingdi; Wang, Lufan

doi:10.1016/j.cam.2018.10.038

Cited by 48 publications

(41 citation statements)

References 32 publications

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“…Example 6 (Reference [46]) [26,43]) (20,5) 11.9538 8.9802 (35,10) 74.8853 56.7866 (37,9) 77.1476 45.6324 (45,8) 86.7174 65.6845 (46,5) 44.2502 32.2150 (60, 11) 315.659 216.534…”

Section: Example 5 (Reference [45])mentioning

confidence: 99%

“…In the last several decades, many algorithms have been developed for globally solving the (QPWQC) and its special cases, such as branch-and-bound method [12,13], approximation approach [14], robust approach [15], branch-reduce-bound algorithm [16][17][18][19], geometric programming approach [20][21][22][23], and others. Except for the above approaches, some global optimization algorithms [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] for linear multiplicative programming problems and generalized linear fractional programming problems can be used to solve the quadratic programs with quadratic constraints (QPWQC) considered in this paper.…”

Section: Introductionmentioning

confidence: 99%

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An Effective Global Optimization Algorithm for Quadratic Programs with Quadratic Constraints

2019

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This paper will present an effective algorithm for globally solving quadratic programs with quadratic constraints. In this algorithm, we propose a new linearization method for establishing the linear programming relaxation problem of quadratic programs with quadratic constraints. The proposed algorithm converges with the global optimal solution of the initial problem, and numerical experiments show the computational efficiency of the proposed algorithm.

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“…Example 6 (Reference [46]) [26,43]) (20,5) 11.9538 8.9802 (35,10) 74.8853 56.7866 (37,9) 77.1476 45.6324 (45,8) 86.7174 65.6845 (46,5) 44.2502 32.2150 (60, 11) 315.659 216.534…”

Section: Example 5 (Reference [45])mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Effective Global Optimization Algorithm for Quadratic Programs with Quadratic Constraints

2019

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“…Recently, Shen and Wang [18] also proposed a full polynomial time approximation algorithm for resolving the problem GLMP globally, but there is no acceleration technique. Moreover, for a more comprehensive overview of the GLMP, we encourage the readers to go through the more detailed literature [8,[19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…By using the definition of δ and formulas (20) and (21), one can infer that formulas (15) and (16) hold.…”

mentioning

confidence: 99%

An Efficient Polynomial Time Algorithm for a Class of Generalized Linear Multiplicative Programs with Positive Exponents

Zhang

Gao

Liu

et al. 2021

Mathematical Problems in Engineering

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This paper explains a region-division-linearization algorithm for solving a class of generalized linear multiplicative programs (GLMPs) with positive exponent. In this algorithm, the original nonconvex problem GLMP is transformed into a series of linear programming problems by dividing the outer space of the problem GLMP into finite polynomial rectangles. A new two-stage acceleration technique is put in place to improve the computational efficiency of the algorithm, which removes part of the region of the optimal solution without problems GLMP in outer space. In addition, the global convergence of the algorithm is discussed, and the computational complexity of the algorithm is investigated. It demonstrates that the algorithm is a complete polynomial time approximation scheme. Finally, the numerical results show that the algorithm is effective and feasible.

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“…We investigate the following generalized linear multiplicative programming problem: all bounded linear (affine) functions defined on X , A ∈ R m×n , b ∈ R m , X is a bounded polyhedron set. Because the problem (MP) have a wide of applications in microeconomics [1], data mining/pattern recognition [2], plant layout design [3], system reliability analysis and optimization [4]- [10], optimal resource allocation for Power-Efficient MC-NOMA [11] and…”

Section: Introductionmentioning

confidence: 99%

An Efficient Outer Space Algorithm for Generalized Linear Multiplicative Programming Problem

et al. 2020

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Base on the outer space search and the branch-and-bound framework, this paper presents an efficient outer space branch-and-bound algorithm for globally solving generalized linear multiplicative programming problem. First of all, we convert the problem into an equivalent problem. Then, by utilizing a direct relaxation method, we establish the linear relaxed problem to compute the lower bound of the global optimal value of the equivalent problem. By subsequently subdividing the initial outer space rectangle and solving a series of linear relaxed problems, the proposed algorithm is convergent to the global optimal solution of the primal problem. Finally, compared with some known algorithms, numerical experiments are given to demonstrate the feasibility and effectiveness of the proposed algorithm. INDEX TERMS Generalized linear multiplicative programming problem, global optimization, linear relaxed problem, branch-and-bound algorithm.

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Range division and linearization algorithm for a class of linear ratios optimization problems

Cited by 48 publications

References 32 publications

An Effective Global Optimization Algorithm for Quadratic Programs with Quadratic Constraints

An Effective Global Optimization Algorithm for Quadratic Programs with Quadratic Constraints

An Efficient Polynomial Time Algorithm for a Class of Generalized Linear Multiplicative Programs with Positive Exponents

An Efficient Outer Space Algorithm for Generalized Linear Multiplicative Programming Problem

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