A new bound-and-reduce approach of nonconvex quadratic programming problems

Gao, Yuelin; Wei, Fei

doi:10.1016/j.amc.2014.10.077

Cited by 4 publications

(4 citation statements)

References 17 publications

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“…As in Tables 4.1 and 4.6-4.9, the symbol for the header line means: Solution: the optimal solution; Optimum: the optimal value; Iter: the number of iterations; Time: the CPU running time in seconds; BBA: the proposed algorithm; OSBBA: the algorithm in [36]; BRA: the algorithm in [11]; Avg.iter: the average number of iterations of the correlation algorithm for solving the 15 test problems; Avg.time: the average CPU running time(s) spent by the relevant algorithm for 15 test problems; Avg.Val: the average optimal value obtained from 15 test problems with relevant algorithm; "-": the algorithm cannot solve the problem in 3600 seconds for all cases.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Firstly, it must be pointed out that the algorithms in [11,18,19,22,23,34,36,46,47] are all branch-and-bound algorithms, and the branching operations of the algorithms in [11,18,34,46] occur in the n-dimensional space where the decision variables are located. Moreover, two wellknown global optimization solvers, SCIP and BARON, which are employed to solve mixed integer (linear or nonlinear) programming problems, are also mainly integrated on the branchand-bound algorithm framework that performs branching operations in n-dimensional space.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Also, the QCQP is a subclass of MIQCQP. For solving the problem MIQCQP, Zhao and Liu [46] and Gao and Wei [11] proposed a series of branch-and-bound algorithms, all of which adopted equivalent transformation to construct the relaxation programming subproblem to obtain the optimal solution. Pai and Alberto [7] developed an approximate algorithm, which can find ǫ-approximate solutions to the MIQCQP problem with concave quadratic objective function, and the running time of this algorithm is polynomial in the size of the problem and in 1/ǫ, as long as the number of integer variables and negative eigenvalues of the objective function are fixed.…”

Section: Introductionmentioning

confidence: 99%

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A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

Zhang¹,

Gao²,

Huang³

2024

JCM

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The mixed-integer quadratically constrained quadratic fractional programming (MIQC-QFP) problem often appears in various fields such as engineering practice, management science and network communication. However, most of the solutions to such problems are often designed for their unique circumstances. This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP. We first convert the MIQC-QFP into an equivalent generalized bilinear fractional programming (EIGBFP) problem with integer variables. Secondly, we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively, and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator. After that, combining rectangular adjustment-segmentation technique and midpointsampling strategy with the branch-and-bound procedure, an efficient algorithm for solving MIQCQFP globally is proposed. Finally, a series of test problems are given to illustrate the effectiveness, feasibility and other performance of this algorithm.

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Section: Numerical Experimentsmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

Zhang¹,

Gao²,

Huang³

2024

JCM

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“…In part, this is because the quadratically constrained quadratic programs problem finds a wide range of applications in management science and engineering, product subassembly, production programs, portfolio decision optimization, chance problem, production design, finance and economy, etc. (see [1][2][3][4][5][6][7]). In particular, many practical problems (such as stochastic programs problem, packing problem, 0-1 programs problem, etc.…”

Section: Introductionmentioning

confidence: 99%

Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

et al. 2017

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This paper presents a branch-delete-bound algorithm for effectively solving the global minimum of quadratically constrained quadratic programs problem, which may be nonconvex. By utilizing the characteristics of quadratic function, we construct a new linearizing method, so that the quadratically constrained quadratic programs problem can be converted into a linear relaxed programs problem. Moreover, the established linear relaxed programs problem is embedded within a branch-and-bound framework without introducing any new variables and constrained functions, which can be easily solved by any effective linear programs algorithms. By subsequently solving a series of linear relaxed programs problems, the proposed algorithm can converge the global minimum of the initial quadratically constrained quadratic programs problem. Compared with the known methods, numerical results demonstrate that the proposed method has higher computational efficiency.

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