Finite algorithm for generalized linear multiplicative programming

Schaible, Siegfried; Sodini, Claudio

doi:10.1007/bf02192573

Cited by 60 publications

(24 citation statements)

References 3 publications

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“…Such problems arise in a variety of applications, including economic analysis [12], bond portfolio optimization [16], optimization of geometrical objects [19], and VLSI chip design [20]. In recent years, a number of algorithms have been proposed for globally solving various types of multiplicative and generalized multiplicative programming problems (see, e.g., [7,14,17,22,27,32], the survey in [18], and references therein).…”

Section: Applicationsmentioning

confidence: 99%

Concave envelopes of monomial functions over rectangles

Benson

2004

Naval Research Logistics

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Abstract:The construction of convex and concave envelopes of real-valued functions has been of interest in mathematical programming for over 3 decades. Much of this interest stems from the fact that convex and concave envelopes can play important roles in algorithms for solving various discrete and continuous global optimization problems. In this article, we use a simplicial subdivision tool to present and validate the formula for the concave envelope of a monomial function over a rectangle. Potential algorithmic applications of this formula are briefly indicated.

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Section: Applicationsmentioning

confidence: 99%

Concave envelopes of monomial functions over rectangles

Benson

2004

Naval Research Logistics

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“…. ; p, and when the constrained domain is a polyhedral set, the NOP problem is called a generalized linear multiplicative programming problem, and several algorithms have been proposed for solving this type of problem in [10][11][12][13][14]. For the parameters p > 1;T j ¼ 2; c j1 ¼ 1 and c j2 ¼ À1;…”

Section: Introductionmentioning

confidence: 99%

Effective algorithm for solving the generalized linear multiplicative problem with generalized polynomial constraints

Jiao

Liu

Zhao

2015

Applied Mathematical Modelling

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Available online xxxxKeywords: Branch and bound Generalized linear multiplicative problem Global optimization Linear lower bound relaxation problem a b s t r a c tIn this study, we propose a novel global optimization algorithm for effectively solving the generalized linear multiplicative problem with generalized polynomial constraints. Based on the branch and bound scheme, the algorithm is implemented by solving its equivalent generalized geometric programming problem. In the algorithm, lower bounds are obtained by solving a sequence of linear lower bound relaxation problems, which can be derived using a new linearization technique. Finally, we prove the global convergence of the algorithm and some numerical results are presented that demonstrate the computational advantages of the proposed algorithm.

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“…In the last decades, many algorithms have been intended for solving the generalized linear multiplicative programming problem, such as parametric simplex algorithms [3,4], quadratic programming algorithms [5][6][7][8][9], rectangle branchand-bound algorithms [10,11], approximate algorithms [12,13], finite algorithm [14], outcome space algorithm [15], cutting plane algorithm [16], heuristic algorithm [17], monotonic 2 Journal of Control Science and Engineering optimization algorithms [18,19], and simplicial branch-andbound algorithm [20]. Although there exist some algorithms which can be used to solve the generalized linear multiplicative programming problem, as far as we know, it is still necessary to propose a more efficient algorithm for globally solving (GAMP).…”

Section: Introductionmentioning

confidence: 99%

An Out Space Accelerating Algorithm for Generalized Affine Multiplicative Programs Problem

Cai

Tang²,

Yin

et al. 2017

Journal of Control Science and Engineering

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This paper presents an out space branch-and-bound algorithm for solving generalized affine multiplicative programs problem. Firstly, by introducing new variables and constraints, we transform the original problem into an equivalent nonconvex programs problem. Secondly, by utilizing new linear relaxation technique, we establish the linear relaxation programs problem of the equivalent problem. Thirdly, based on the out space partition and the linear relaxation programs problem, we construct an out space branch-and-bound algorithm. Fourthly, to improve the computational efficiency of the algorithm, an out space reduction operation is employed as an accelerating device for deleting a large part of the investigated out space region. Finally, the global convergence of the algorithm is proved, and numerical results demonstrate the feasibility and effectiveness of the proposed algorithm.

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Finite algorithm for generalized linear multiplicative programming

Cited by 60 publications

References 3 publications

Concave envelopes of monomial functions over rectangles

Concave envelopes of monomial functions over rectangles

Effective algorithm for solving the generalized linear multiplicative problem with generalized polynomial constraints

An Out Space Accelerating Algorithm for Generalized Affine Multiplicative Programs Problem

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