On the minimization of a class of generalized linear functions on a flow polytope

Cambini, Riccardo; Sodini, Claudio

doi:10.1080/02331934.2013.852548

Cited by 23 publications

(3 citation statements)

References 15 publications

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“…, p. This issue AMP has attracted widespread attention from many scholars over the years.There are two main reasons. One is that it has a wide application background, such as multiple-objective decision [1,2],computer vision [3,4],decision tree optimization [5], quantitative management science applications [6,7], control and engineering optimization [8][9][10][11], network flow optimization [12,13], robust optimization [14], system reliability analysis [15], and so on.On the other hand, since problem (AMP) is a non-convex optimization problem, it has many local optimal solutions. Therefore, this problem is a high-value problem with considerable application background and extremely challenging.…”

Section: Introductionmentioning

confidence: 99%

An outcome space branch and bound algorithm for affine multiplicative problems using piecewise linear approximation technique

Hu,

Wu,

et al. 2024

Preprint

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This paper presents an efficient algorithm for solving a class of affine multiplication programs(AMP). In order to obtain the global optimal solution of the problem, we first transform the problem into an equivalent problem by introducing auxiliary variables. Secondly, we utilize a new piecewise linear approximation technology to systematically transform the problem into a series of linear relaxation programming problems to obtain a reliable lower bound of the optimal value of the problem. Hence, according to the characteristics of the problem and the structure of the branch-and-bound framework, some outer space acceleration techniques are constructed to improve the convergence speed of the algorithm. In addition, by analyzing the computational complexity of the algorithm, an estimate of the maximum number of iterations of the algorithm is given. Finally, numerical results verify the effectiveness and robustness of the algorithm.

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Section: Introductionmentioning

confidence: 99%

An outcome space branch and bound algorithm for affine multiplicative problems using piecewise linear approximation technique

Hu,

Wu,

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…The problem (MP) and its special form are worth studying, and which have attracted much attention from scholars. The first reason is that the problem (MP) and its special form have a wide of practical applications, such as network flows [3,4], VLISI chip design [6], robust optimization [26], decision tree optimization [1], financial optimization [19,24], and so on [10,14,15]. The second reason is that the problem (MP) and its special form are all non-convex programming problem, which generally contain multiple local optimal solutions that are not global optimal, so that there are many computational difficulties.…”

Section: Introductionmentioning

confidence: 99%

Image space branch-reduction-bound algorithm for globally minimizing a class of multiplicative problems

et al. 2022

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This paper presents an image space branch-reduction-bound algorithm for solving a class of multiplicative problems (MP). First of all, by introducing auxiliary variables and taking the logarithm of the objective function, an equivalent problem (EP) of the problem (MP) is obtained. Next, by using a new linear relaxation technique, the parametric linear relaxation programming (PLRP) of the equivalence problem (EP) can be established for acquiring the lower bound of the optimal value to the problem (EP). Based on the characteristics of the objective function of the equivalent problem and the structure of the branch-and-bound algorithm, some region reduction techniques are constructed for improving the convergence speed of the algorithm. Finally, the global convergence of the algorithm is proved and its computational complexity is estimated, and numerical experiments are reported to indicate the higher computational performance of the algorithm.

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“…e problem (MP) comes from various application elds, for example, decision tree optimization [1], multipleobjective decision [2,3], robust optimization [4], control and engineering optimization [5][6][7][8][9], computer vision [10,11], network ow optimization [12][13][14], food science engineering, and big data analysis. at is to say, the problem is useful in many aspects, so it is of great importance to develop an e cient algorithm for the problem (MP).…”

Section: Introductionmentioning

confidence: 99%

Image Space Accelerating Algorithm for Solving a Class of Multiplicative Programming Problems

Zhou

Gao

et al. 2022

Mathematical Problems in Engineering

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This paper interprets an image space accelerating branch and bound algorithm for globally solving a class of multiplicative programming problems (MP). In this algorithm, in order to obtain the global optimal solution, the problem (MP) is transformed into an equivalent problem (P2) by introducing new variables. By utilizing new linearizing relaxation technique, the problem (P2) can be converted into a series of linear relaxation programming problems, which provide the reliable lower bound in the branch and bound search. Meanwhile, an image space accelerating method is constructed to improve the computational performance of the algorithm by deleting the subintervals which have no global optimal solution. Furthermore, the global convergence of the algorithm is proved. The computational complexity of the algorithm is analyzed, and the maximum iterations of the algorithm are estimated. Finally, numerical experimental results show that the algorithm is robust and efficient.

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On the minimization of a class of generalized linear functions on a flow polytope

Cited by 23 publications

References 15 publications

An outcome space branch and bound algorithm for affine multiplicative problems using piecewise linear approximation technique

An outcome space branch and bound algorithm for affine multiplicative problems using piecewise linear approximation technique

Image space branch-reduction-bound algorithm for globally minimizing a class of multiplicative problems

Image Space Accelerating Algorithm for Solving a Class of Multiplicative Programming Problems

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