Global Optimality Conditions in Nonconvex Optimization

Strekalovsky, Alexander S.

doi:10.1007/s10957-016-0998-7

Cited by 28 publications

(21 citation statements)

References 9 publications

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“…Global optimization of D.C.for error minimization. The constraint function y = Aζ in 4 is a typical nonconvex optimality problem, where the goal function with and the inequality constraints represented by the difference of convex functions discussed in [10]. And the goal function in 4 can be rewriter as…”

Section: 2mentioning

confidence: 99%

Error minimization with global optimization for difference of convex functions

Deng¹,

Hu²

2019

Discrete &Amp; Continuous Dynamical Systems - S

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In this paper, a hybrid positioning method based on global optimization for difference of convex functions (D.C.) with time of arrival (TOA) and angle of arrival (AOA) measurements are proposed. Traditional maximum likelihood (ML) formulation for indoor localization is a nonconvex optimization problem. The relaxation methods can?t provide a global solution. We establish a D.C. model for TOA/AOA fusion positioning model and give a solution with a global optimization. Simulations based on TC-OFDM signal system show that the proposed method is efficient and more robust as compared to the existing ML estimation and convex relaxation.

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Section: 2mentioning

confidence: 99%

Error minimization with global optimization for difference of convex functions

Deng¹,

Hu²

2019

Discrete &Amp; Continuous Dynamical Systems - S

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“…, m, are simply convex or generally d.c. functions, it can readily be observed that Problem (P α ) belongs to the class of d.c. minimization. As a consequence, in order to solve Problem (P α ), we can apply the Global Search Theory [26,28].…”

Section: The DC Programming Approach To Fractional Programmentioning

confidence: 99%

“…In [12] it was proved that for any solution (x * , α * ) ∈ IR n ×IR m to Problem (P c ), the point x * will be a solution to Problem (P f ). Therefore, we can solve Problem (P c ) using the exact penalization approach for d.c. optimization developed in [28] as well as the global search theory for solving the d.c. constraints problem [26].…”

Section: The DC Programming Approach To Fractional Programmentioning

confidence: 99%

“…The second one deals with another auxiliary problem over nonconvex inequality constraints. Both auxiliary problems are d.c. optimization problems, which allows us to apply the Global Optimization Theory [26,27,28,29], recently successfully applied to another practical problem arising in mineral processing industry of Mongolia [10,16]. In this paper we develop a two-component algorithm based on the global optimality conditions for d.c. optimization problems [26,28] to solve the average cost minimization problem for power companies of Mongolia.…”

Section: Introductionmentioning

confidence: 99%

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Fractional programming approach to a cost minimization problem in electricity market

Gruzdeva

Enkhbat

Tungalag

2019

YUGOSLAV J OPERATION

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This paper was motivated by a practical optimization problem that appeared in electricity market of Mongolia. We consider the total average cost minimization problem of power companies of the Ulaanbaatar city. By solving an identification problem, we developed a fractional model that quite adequately represents the real data. The obtained problem turned out to be a fractional minimization problem over a box constraint, and to solve it, we propose a method that employs the global search theory for d.c. minimization.

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“…It is interesting to note that in [16] an approximation scheme of the step function is cast into a DC (Difference of Convex) framework, providing thus the opportunity of resorting to the algorithmic machinery for dealing with such class of nonconvex problems. An early survey on properties and relevance of such class of functions is in [12] (see also [22]).…”

Section: Introductionmentioning

confidence: 99%

Feature selection in SVM via polyhedral k-norm

2019

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We treat the Feature Selection problem in the Support Vector Machine (SVM) framework by adopting an optimization model based on use of the 0 pseudo-norm. The objective is to control the number of non-zero components of normal vector to the separating hyperplane, while maintaining satisfactory classification accuracy. In our model the polyhedral norm. [k] , intermediate between. 1 and. ∞, plays a significant role, allowing us to come out with a DC (Difference of Convex) optimization problem that is tackled by means of DCA algorithm. The results of several numerical experiments on benchmark classification datasets are reported.

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Global Optimality Conditions in Nonconvex Optimization

Cited by 28 publications

References 9 publications

Error minimization with global optimization for difference of convex functions

Error minimization with global optimization for difference of convex functions

Fractional programming approach to a cost minimization problem in electricity market

Feature selection in SVM via polyhedral k-norm

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