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A neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraints

NEURAL NETWORKS 2019年 109卷 147-158页

作者： Liu, Na Qin, Sitian Harbin Inst Technol Dept Math Weihai Peoples R China

This paper presents a neurodynamic approach to nonlinear optimization problems with affine equality and convex inequality constraints. The proposed neural network endows with a time-varying auxiliary function, which can guarantee that the state of the neural network enters the feasible region in finite time and remains there thereafter. Moreover, the state with any initial point is shown to be convergent to the critical point set when the objective function is generally nonconvex. Especially, when the objective function is pseudoconvex (or convex), the state is proved to be globally convergent to an optimal solution of the considered optimization problem. Compared with other neural networks for related optimization problems, the proposed neural network in this paper has good convergence and does not depend on some additional assumptions, such as the assumption that the inequality feasible region is bounded, the assumption that the penalty parameter is sufficiently large and the assumption that the objective function is lower bounded over the equality feasible region. Finally, some numerical examples and an application in real-time data reconciliation are provided to display the well performance of the proposed neural network. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： nonlinear optimization problems Recurrent neural network Lyapunov function Global convergence

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Finite-time recurrent neural networks for solving nonlinear optimization problems and their application

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NEUROCOMPUTING 2016年 177卷 120-129页

作者： Miao, Peng Shen, Yanjun Li, Yujiao Bao, Lei China Three Gorges Univ Hubei Prov Collaborat Innovat Ctr New Energy Micr Yichang 443002 Peoples R China Zhengzhou Sci & Technol Univ Dept Basic Courses Zhengzhou 450064 Hennan Peoples R China China Three Gorges Univ Coll Sci Yichang 443002 Peoples R China

This paper focuses on finite-time recurrent neural networks with continuous but non-smooth activation function solving nonlinearly constrained optimization problems. Firstly, definition of finite-time stability and finite-time convergence criteria are reviewed. Secondly, a finite-time recurrent neural network is proposed to solve the nonlinear optimization problem. It is shown that the proposed recurrent neural network is globally finite-time stable under the condition that the Hessian matrix of the associated Lagrangian function is positive definite. Its output converges to a minimum solution globally and finite time, which means that the actual minimum solution can be derived in finite-time period. In addition, our recurrent neural network is applied to a hydrothermal scheduling problem. Compared with other methods, a lower consumption scheme can be derived in finite-time interval. At last, numerical simulations demonstrate the superiority and effectiveness of our proposed neural networks by solving nonlinear optimization problems with inequality constraints. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Finite-time stable Recurrent neural network nonlinear optimization problems Continuous but non-smooth Hydrothermal scheduling problem

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nonlinear optimization VIA NOVEL NEURAL NETWORK METHODS

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JOURNAL OF INDUSTRIAL AND MANAGEMENT optimization 2025年第4期21卷 2472-2489页

作者： Teng, Jiao Yiu, Ka fai cedric Hong Kong Polytech Univ Dept Appl Math Hong Kong Peoples R China

This paper introduces a novel approach for solving high-dimensional nonlinear optimization problems by integrating neural networks into the optimization process. The method leverages the capabilities of neural networks to efficiently handle complex, high-dimensional data and to approximate discrete numerical solutions of nonlinear optimization problems using continuous functions. By combining the nonlinear mapping ability of neural networks with iterative optimization algorithms, the proposed approach provides a superior method to solve nonlinear optimization problems. The paper demonstrates the adaptability of neural network-based solution methods in solving various nonlinear optimization problems and illustrates that the method can be applied to many different problem scenarios. The effectiveness and correctness of the proposed method are demonstrated through examples.

关键词： nonlinear optimization problems Neural networks

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An equivalent nonlinear optimization model with triangular low-rank factorization for semidefinite programs

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optimization METHODS & SOFTWARE 2023年第6期38卷 1296-1310页

作者： Yamakawa, Yuya Ikegami, Tetsuya Fukuda, Ellen H. H. Yamashita, Nobuo Kyoto Univ Grad Sch Informat Yoshida HonmachiSakyo Ku Kyoto 6068501 Japan Yahoo Japan Corp Data & Sci Solut Grp Technol Grp Chiyoda Ku Tokyo Japan

In this paper, we propose a new nonlinear optimization model to solve semidefinite optimization problems (SDPs), providing some properties related to local optimal solutions. The proposed model is based on another nonlinear optimization model given by [S. Burer and R. Monteiro, A nonlinear programming algorithm for solving semidefinite programs via low-rank factorization, Math. Program. Ser. B 95 (2003), pp. 329-357], but it has several nice properties not seen in the existing one. Firstly, the decision variable of the proposed model is a triangular low-rank matrix. Secondly, the existence of a strict local optimum of the proposed model is guaranteed under some conditions, whereas the existing model has no strict local optimum. In other words, it is difficult to construct solution methods equipped with fast convergence using the existing model. We also present some numerical results, showing that the use of the proposed model allows to deliver highly accurate solutions.

关键词： Semidefinite optimization problems nonlinear optimization problems sequential quadratic programming method triangular low-rank factorization

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Quantum-Behaved Particle Swarm optimization Algorithm Based on the Two-Body Problem

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Chinese Journal of Electronics 2019年第3期28卷 569-576页

作者： YAN Tao LIU Fengxian Institute of Big Data Science and Industry Shanxi University School of Computer and Information Technology Shanxi University Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education Guangzhou Institute of Electronic Technology Chinese Academy of Sciences University of Chinese Academy of Sciences

The present study proposes an improved Quantum-behaved particle swarm optimization algorithm based on the two-body problem model(QTPSO) for solving the problem that other quantum-behaved particle swarm optimization algorithms easily converge on local optimal solutions when solving complex nonlinear problems. In the proposed QTPSO algorithm, particles are categorised as core particles and edge particles. Once the position of the core particle is determined, the edge particle appears in the vicinity of the attractor exhibiting a high probability, and the attractor is obtained through the random weighted sum of the core particle and the optimal mean position. Through simulation of the motion of these two particles by applying the interaction of the particles in the two-body problem, this mechanism not only improves the diversity of the population, but also enhances the local search capacity. To validate the proposed algorithm, three groups of experimental results were obtained to compare the proposed algorithm with other swarm intelligence algorithms. The experimental results indicate the superiority of the QTPSO algorithm.

关键词： Quantum-behaved particle swarm optimization Two-body problem Quantum potential well Wave function nonlinear optimization problems

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Sequential linear programming and particle swarm optimization for the optimization of energy districts

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ENGINEERING optimization 2019年第1期51卷 84-100页

作者： Riccietti, Elisa Bellavia, Stefania Sello, Stefano Univ Firenze Dipartimento Matemat & Informat Ulisse Dini Florence Italy Univ Firenze Dipartimento Ingn Ind Florence Italy Enel Ingn & Ric Pisa Italy IRIT Toulouse France

This article deals with the optimization of energy resource management of industrial districts, with the aim of minimizing customer energy expenses. A model of the district is employed, whose optimization gives rise to a nonlinear constrained optimization problem. Here the focus is on its numerical solution. Two different methods are considered: a sequential linear programming method and a particle swarm optimization method. Efficient implementations of both approaches are devised and the results of the tests performed on several energetic districts are reported, including a real case study.

关键词： nonlinear optimization problems sequential linear programming particle swarm optimization energy districts penalty functions

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OpenMP Genetic Algorithm for Continuous nonlinear Large-Scale optimization problems 5th

OpenMP Genetic Algorithm for Continuous Nonlinear Large-Scal...

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5th International Conference on Soft Computing for Problem Solving (SocProS)

作者： Umbarkar, A. J. Walchand Coll Engn Dept Informat Technol Sangli MS India

ISBN: (纸本)9789811004513;9789811004506

Genetic algorithms (GAs) are one of the evolutionary algorithms for solving continuous nonlinear large-scale optimization problems. In an optimization problem, when dimension size increases, the size of search space increases exponentially. It is quite difficult to explore and exploit such huge search space. GA is highly parallelizable optimization algorithm;still there is a challenge to use all the cores of multicore (viz. Dual core, Quad core, and Octa cores) systems. The paper analyzes the parallel implementation of SGA (Simple GA) called as OpenMP GA. OpenMP (Open Multi-Processing) GA attempts to explore and exploit the search space on the multiple cores' system. The performance of OpenMP GA is compared with SGA with respect to time required and cores utilized for obtaining optimal solution. The results show that the performance of the OpenMP GA is remarkably superior to that of the SGA in terms of execution time and CPU utilization. In case of OpenMP GA, CPU utilization is almost double for continuous nonlinear large-scale test problems for the given system configuration.

关键词： Function optimization Genetic algorithm (GA) Open multi-processing (OpenMP) nonlinear optimization problems optimization benchmarks functions

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Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2011年第5期235卷 1446-1453页

作者： Abd-El-Wahed, W. F. Mousa, A. A. El-Shorbagy, M. A. Shebin El Kom Minufiya Univ Fac Engn Dept Basic Engn Sci Shibin Al Kawm Egypt Shebin El Kom Minufiya Univ Fac Comp & Informat Shibin Al Kawm Egypt

Heuristic optimization provides a robust and efficient approach for solving complex real-world problems. The aim of this paper is to introduce a hybrid approach combining two heuristic optimization techniques, particle swarm optimization (PSO) and genetic algorithms (GA). Our approach integrates the merits of both GA and PSO and it has two characteristic features. Firstly, the algorithm is initialized by a set of random particles which travel through the search space. During this travel an evolution of these particles is performed by integrating PSO and GA. Secondly, to restrict velocity of the particles and control it, we introduce a modified constriction factor. Finally, the results of various experimental studies using a suite of multimodal test functions taken from the literature have demonstrated the superiority of the proposed approach to finding the global optimal solution. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Particle swarm optimization Genetic algorithm nonlinear optimization problems Constriction factor

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p-regular nonlinearity: tangency at singularity in degenerate optimization problems

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2017年第3期86卷 485-500页

作者： Bednarczuk, Ewa M. Tretyakov, Alexey Syst Res Inst Ul Newelska 6 PL-01447 Warsaw Poland Siedlce Univ Nat Sci & Humanities Fac Sci Siedlce Poland Russian Acad Sci Dorodnicyn Comp Ctr Moscow Russia Warsaw Univ Technol Koszykowa 75 PL-00662 Warsaw Poland

We investigate description of the tangent cone to the null set of a mapping F at a given point in the case when F is degenerate at . To this aim we introduce the concept of modified 2-regular mappings, which generalizes the concept of p-regular mappings. Our main result provides the description of the tangent cone to the null set of modified 2-regular mappings. With the help of this result we derive new optimality conditions for a wide class of optimization problems with equality constraints.

关键词： Tangent cone Degenerate mapping p-regularity nonlinear optimization problems Optimality conditions

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A new optimization algorithm based on chaotic maps and golden section search method

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2016年 50卷 201-214页

作者： Koupaei, J. Alikhani Hosseini, S. M. M. Ghaini, F. M. Maalek Yazd Univ Dept Math POB 89195-74 Yazd Iran Payame Noor Univ Dept Math POB 19395-3697 Tehran Iran Shahid Bahonar Univ Kerman Dept Appl Math Kerman Iran

In this paper, we introduced a practical version of golden section search algorithm to optimize multi/uni-modal objective functions. Accordingly, this study presented a novel algorithm combining the capabilities of chaotic maps and the golden section search method in order to solve nonlinear optimization problems. To this end, a bipartite experimental procedure was utilized. (1) Chaotic convertor as a global search: the search space of a problem can be converted to a local search space using the chaotic concept. The chaotic maps can explore a sub-space to satisfy uni-modal condition for the golden section search (GSS) algorithm. (2) GSS as a local search: the n-D GSS applies over the achieved search space to exploit an optimal solution. In order to study the performance of the proposed algorithm, twenty benchmark functions and one real world problem were employed. The experimental results revealed that the proposed algorithm was an effective and efficient optimization algorithm in comparison with some state-of-the-art methods. The proposed algorithm performs effectively for the engineering applications such as the gear train deign problem. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： nonlinear optimization problems Golden section search method Chaotic optimization algorithms Meta-heuristic algorithms Chaotic maps

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