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1
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A note on strong pseudoconvexity

100%
Ivanov V.
Open Mathematics
|
2008
|
tom 6
|
nr 4
576-580
EN
A strongly pseudoconvex function is generalized to non-smooth settings. A complete characterization of the strongly pseudoconvex radially lower semicontinuous functions is obtained.
2
Content available remote

Outcome space range reduction method for global optimization of sum of affine ratios problem

100%
Jiao H., Liu S., Yin J., Zhao Y.
Open Mathematics
|
2016
|
tom 14
|
nr 1
736-746
EN
Many algorithms for globally solving sum of affine ratios problem (SAR) are based on equivalent problem and branch-and-bound framework. Since the exhaustiveness of branching rule leads to a significant increase in the computational burden for solving the equivalent problem. In this study, a new range reduction method for outcome space of the denominator is presented for globally solving the sum of affine ratios problem (SAR). The proposed range reduction method offers a possibility to delete a large part of the outcome space region of the denominators in which the global optimal solution of the equivalent problem does not exist, and which can be seen as an accelerating device for global optimization of the (SAR). Several numerical examples are presented to demonstrate the advantages of the proposed algorithm using new range reduction method in terms of both computational efficiency and solution quality.
3
Content available remote

A new branch and bound algorithm for minimax ratios problems

100%
Zhao Y., Liu S., Jiao H.
Open Mathematics
|
2017
|
tom 15
|
nr 1
840-851
EN
This study presents an efficient branch and bound algorithm for globally solving the minimax fractional programming problem (MFP). By introducing an auxiliary variable, an equivalent problem is firstly constructed and the convex relaxation programming problem is then established by utilizing convexity and concavity of functions in the problem. Other than usual branch and bound algorithm, an adapted partition skill and a practical reduction technique performed only in an unidimensional interval are incorporated into the algorithm scheme to significantly improve the computational performance. The global convergence is proved. Finally, some comparative experiments and a randomized numerical test are carried out to demonstrate the efficiency and robustness of the proposed algorithm.
4
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Branch-delete-bound algorithm for globally solving quadratically constrained quadratic programs

76%
Hou Z., Jiao H., Cai L., Bai C.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1212-1224
EN
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.
5
Content available remote

Nature–inspired metaheuristic algorithms to find near–OGR sequences for WDM channel allocation and their performance comparison

76%
Bansal S., Gupta N., Singh A. K.
Open Mathematics
|
2017
|
tom 15
|
nr 1
520-547
EN
Nowadays, nature–inspired metaheuristic algorithms are most powerful optimizing algorithms for solving the NP–complete problems. This paper proposes three approaches to find near–optimal Golomb ruler sequences based on nature–inspired algorithms in a reasonable time. The optimal Golomb ruler (OGR) sequences found their application in channel–allocation method that allows suppression of the crosstalk due to four–wave mixing in optical wavelength division multiplexing systems. The simulation results conclude that the proposed nature–inspired metaheuristic optimization algorithms are superior to the existing conventional and nature–inspired algorithms to find near–OGRs in terms of ruler length, total optical channel bandwidth, computation time, and computational complexity. Based on the simulation results, the performance of proposed different nature–inspired metaheuristic algorithms are being compared by using statistical tests. The statistical test results conclude the superiority of the proposed nature–inspired optimization algorithms.
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