Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique

Malek, Alaeddin; Hosseinipour-Mahani, N.

doi:10.14736/kyb-2015-5-0890

Cited by 6 publications

(7 citation statements)

References 28 publications

(32 reference statements)

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“…then [TP-K DN N ] can be used to approximate problem (34), we obtain a bound of −12.83, which provides better bounds than SDP relaxation and completely positive relaxation on problem (33). We also add the valid inequalities x 2 f 2 (x) ≤ 0, x 2 1 f 1 (x) ≤ 0 directly to problem (33) by reformulating problem (34) as a quadratic program by adding additional variables and constraints as in (15):…”

mentioning

confidence: 93%

“…For example, to address the solution of QPs, Semidefinite Programming (SDP) [cf., 44] relaxations have been actively used to find good bounds and approximate solutions for general [see, e.g. 15,33,45] and important instances of this problem such as the max-cut problem and the stable set problem (see e.g., [16,17,21,37]). In [24], less computationally expensive second order cone programming (SOCP) [cf.…”

Section: Introductionmentioning

confidence: 99%

“…approximate solutions for general [see, e.g. 15,33,45] and important instances of this problem such as the max-cut problem and the stable set problem (see e.g., [16,17,21,37]). In [24], less computationally expensive second order cone programming (SOCP) [cf., 2] relaxations have also been proposed to approximate non-convex QPs.…”

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confidence: 99%

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Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization

Kuang

Zuluaga

2017

J Glob Optim

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Completely positive (CP) tensors, which correspond to a generalization of CP matrices, allow to reformulate or approximate a general polynomial optimization problem (POP) with a conic optimization problem over the cone of CP tensors. Similarly, completely positive semidefinite (CPSD) tensors, which correspond to a generalization of positive semidefinite (PSD) matrices, can be used to approximate general POPs with a conic optimization problem over the cone of CPSD tensors. In this paper, we study CP and CPSD tensor relaxations for general POPs and compare them with the bounds obtained via a Lagrangian relaxation of the POPs. This shows that existing results in this direction for quadratic POPs extend to general POPs. Also, we provide some tractable approximation strategies for CP and CPSD tensor relaxations. These approximation strategies show that, with a similar computational effort, bounds obtained from them for general POPs can be tighter than bounds for these problems obtained by reformulating the POP as a quadratic POP, which subsequently can be approximated using CP and PSD matrices. To illustrate our results, we numerically compare the bounds obtained from these relaxation approaches on small scale fourth-order degree POPs.

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confidence: 93%

Section: Introductionmentioning

confidence: 99%

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Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization

Kuang

Zuluaga

2017

J Glob Optim

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“…The main purpose of using neural networks for solving various problems is to exploit their parallel processing nature and access to hardware implementations, which make it easier to deal with complex structures of considered problems [12,40]. Following the interesting work of Hopfield and Tank, the theory, methodology, and application of neural networks have been expanded to solve optimization problems [13,14,15,24,30,31,32].There are also several ANN models to solve bilevel problems and MPECs. Sheng et.…”

Section: Introductionmentioning

confidence: 99%

A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints

Ezazipour¹,

Golbabai²

2020

Kybernetika

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“…For example, Beyer and Ogier (1991) and Sun and Feng (2005) proposed two neural network models for unconstrained nonconvex optimization problems. Several neural network were developed for nonconvex quadratic programming problems (Li, Wang, Liang, & Pardalos, 2007;Forti, Nistri, & Quincampoix, 2006;Malek & Hosseinipour-Mahani, 2015). Xia, Feng, and Wang (2008) introduced a recurrent neural network model to solve NCNO problems with inequality constraints.…”

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confidence: 99%

An efficient neurodynamic model to solve nonconvex nonlinear optimization problems and its applications

Moghaddas

Tohidi

2019

Expert Systems

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This paper presents a recurrent neural network for solving nonconvex nonlinear optimization problems subject to nonlinear inequality constraints. First, the p‐power transformation is exploited for local convexification of the Lagrangian function in nonconvex nonlinear optimization problem. Next, the proposed neural network is constructed based on the Karush–Kuhn–Tucker (KKT) optimality conditions and the projection function. An important property of this neural network is that its equilibrium point corresponds to the optimal solution of the original problem. By utilizing an appropriate Lyapunov function, it is shown that the proposed neural network is stable in the sense of Lyapunov and convergent to the global optimal solution of the original problem. Also, the sensitivity of the convergence is analysed by changing the scaling factors. Compared with other existing neural networks for such problem, the proposed neural network has more advantages such as high accuracy of the obtained solutions, fast convergence, and low complexity. Finally, simulation results are provided to show the benefits of the proposed model, which compare to or outperform existing models.

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Solving a class of non-convex quadratic problems based on generalized KKT conditions and neurodynamic optimization technique

Cited by 6 publications

References 28 publications

Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization

Completely positive and completely positive semidefinite tensor relaxations for polynomial optimization

A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints

An efficient neurodynamic model to solve nonconvex nonlinear optimization problems and its applications

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