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Probability-directed random search algorithm for unconstrained optimization problem

APPLIED SOFT COMPUTING 2018年 71卷 165-182页

作者： Al-Muhammed, Muhammed Jassem Abu Zitar, Raed Amer Univ Madaba Fac Informat Technol Madaba Jordan Ajman Univ Ajman Coll Informat Technol Ajman U Arab Emirates

Devising ways for handling problem optimization is an important yet a challenging task. The aims are always for methods that can effectively and quickly discover the global optimum for rather complicated mathematical functions that model real-world settings. Typically these functions are too difficult to discover their global optima because they may (1) lack the continuity and differentiability, (2) have multiple local optima, and (3) have complex expressions. In this paper, we address this challenge by offering an algorithm that combines the random search techniques with both an effective mapping and a dynamic adjustment of its search behavior. Our proposed algorithm automatically builds two types of triangular search directives over the unity intervals: principal and marginal. These search directives guide the search within both the effective regions of the search domain that most likely contain the optimum and the marginal regions of the search domain that less likely contain the optimum. During the search the algorithm monitors the intermediate search results and dynamically adjusts the directives' parameters to quickly move the search towards the optimum. Experiments with our prototype implementation showed that our method can effectively find the global optima for rather complicated mathematical functions chosen from well-known benchmarks, and performed better than other algorithms. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Probability-directed optimization unconstrained optimization problem Global optimum Multiple local optima

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An adaptive restarting RMIL conjugate gradient method and its hybrid version: global convergence and iterative complexity analyses

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2025年 1-22页

作者： Ma, Xuejie Wu, Bin Liu, Pengjie He, Bo Guangzhou Huashang Coll Sch Artificial Intelligence Guangzhou 511300 Peoples R China China Univ Min & Technol Sch Math Xuzhou 221116 Peoples R China Xiangtan Univ Sch Math & Computat Sci Xiangtan 411105 Peoples R China

In this study, we present an adaptive restarting RMIL conjugate gradient (CG) method and its hybrid version for solving unconstrained optimization problems. First, we introduce an effective restarting direction and integrate it into the RMIL CG method. The resulting composite search direction, independent of any line search, possesses the sufficient descent property. Then, by using the hybrid strategy presented in [Applied Mathematical Modelling 39 (2015) 1281-1290], we obtain a hybrid RMIL CG method with a restarting mechanism, whose search direction also has the desired properties. Furthermore, we demonstrate the global convergence of the two proposed methods under conventional assumptions, where the step sizes are determined using the weak Wolfe line search. Additionally, by using the Armijo line search to determine step sizes, we derive the iterative complexity of the obtained methods. Numerical experiments comparing our methods with existing methods confirm their efficiency in addressing unconstrained optimization problems. Finally, we employ the proposed methods for image restoration tasks.

关键词： unconstrained optimization problem RMIL conjugate gradient method Restart mechanism Theoretical property Image restoration

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A novel method for solving universum twin bounded support vector machine in the primal space

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ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE 2025年第1期93卷 131-150页

作者： Moosaei, Hossein Khosravi, Saeed Bazikar, Fatemeh Hladik, Milan Guarracino, Mario Rosario Univ JE Purkyne Fac Sci Dept Informat Usti Nad Labem Czech Republic Charles Univ Prague Fac Math & Phys Sch Comp Sci Dept Appl Math Prague Czech Republic Prague Univ Econ & Business Prague Czech Republic Univ Bojnord Fac Sci Dept Comp Sci Bojnord Iran Univ Guilan Fac Math Sci Dept Appl Math Rasht Iran Charles Univ Prague Fac Math & Phys Dept Appl Math Prague Czech Republic Univ Econ Dept Econometr Prague Czech Republic Univ Cassino & Southern Lazio Campus Folcara Dept Econ & Law Cassino Italy Natl Res Univ Higher Sch Econ Lab Algorithms & Technol Networks Anal Nizhnii Novgorod Russia

In supervised learning, the Universum, a third class that is not a part of either class in the classification task, has proven to be useful. In this study we propose (NU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak {U} $$\end{document}TBSVM), a Newton-based approach for solving in the primal space the optimization problems related to Twin Bounded Support Vector Machines with Universum data (U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak {U} $$\end{document}TBSVM). In the NU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak {U} $$\end{document}TBSVM, the constrained programming problems of U\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak {U} $$\end{document}TBSVM are converted into unconstrained optimization problems, and a generalization of Newton's method for solving the unconstrained problems is introduced. Numerical experiments on synthetic, UCI, and NDC data sets show the ability and effectiveness of the proposed NU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathfrak {U} $$\end{document}TBSVM. We apply the suggested met

关键词： Twin bounded support vector machine Universum Newton's method unconstrained optimization problem

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Two modified DY conjugate gradient methods for unconstrained optimization problems

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APPLIED MATHEMATICS AND COMPUTATION 2020年第0期373卷 125004-000页

作者： Zhu, Zhibin Zhang, Dongdong Wang, Shuo Guilin Univ Elect Technol Guangxi Coll & Univ Key Lab Data Anal & Computat Sch Math & Comp Sci Guilin 541004 Peoples R China Guilin Univ Elect Technol Sch Elect Engn & Automat Guilin 541004 Peoples R China

In this paper, we study the unconstrained optimization problems, and the two modified DY conjugate gradient methods (DDY1 method and DDY2 method) are proposed under the DY conjugate gradient method. By using the standard Wolfe line search, we prove the global convergence of the two methods. The search direction of DDY1 method is descent with the standard Wolfe line search. The search direction generated by the DDY2 method is sufficient descent, in which the property does not depend on any line search. Preliminary numerical results show that the two methods are effective. (C) 2019 Elsevier Inc. All rights reserved.

关键词： unconstrained optimization problem Conjugate gradient method Standard Wolfe line search Global convergence Sufficient descent property

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Two sufficient descent three-term conjugate gradient methods for unconstrained optimization problems with applications in compressive sensing

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2022年第3期68卷 1787-1816页

作者： Liu, Yufeng Zhu, Zhibin Zhang, Benxin Guilin Univ Elect Technol Sch Elect Engn & Automat Guangxi Key Lab Automat Detecting Technol & Instr Guilin 541004 Peoples R China Guilin Univ Elect Technol Sch Math & Comp Sci Guangxi Coll & Univ Key Lab Data Anal & Computat Guilin 541004 Peoples R China

In this paper, we present two new three-term conjugate gradient methods which can generate sufficient descent directions for the large-scale optimization problems. Note that this property is independent of the line search used. We prove that these three-term conjugate gradient methods are global convergence under the Wolfe line search. Numerical experiments and comparisons demonstrate that the proposed algorithms are efficient approaches for test functions. Moreover, we use the proposed methods to solve the l(1) - alpha l(2) regularization problem of sparse signal decoding in compressed sensing, and the results show that our methods have certain advantages over the existing solvers on such problems.

关键词： unconstrained optimization problem Three-term conjugate gradient method Sufficient descent property Global convergence l(1) - alpha l(2) minimization Compressive sensing

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Two spectral conjugate gradient methods for unconstrained optimization problems

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2022年第6期68卷 4821-4841页

作者： Zhu, Zhibin Long, Ai Wang, Tian Guilin Univ Elect Technol Sch Math & Comp Sci Guangxi Coll & Univ Key Lab Data Anal & Computat Guilin 541004 Peoples R China

Two new spectral conjugate gradient methods (ZL1 method and ZL2 method) for solving unconstrained optimization problems are established. Under the standard Wolfe line search, the search direction generated by the ZL1 method is a descent direction. The search direction of the ZL2 method satisfies descent property independent of the line search. The global convergence of the two new methods can be demonstrated under the standard Wolfe line search. Numerical experiments are presented to show that the two methods are effective.

关键词： unconstrained optimization problem Spectral conjugate gradient method Standard Wolfe line search Global convergence

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A Subspace Method for solving unconstrained optimization problems Without Derivatives 8

A Subspace Method for solving Unconstrained Optimization Pro...

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International Conference on Information and Communication Technology Convergence (ICTC)

作者： Zhang, Yimeng He, Zuguo Beijing Univ Posts & Telecommun Sch Sci Beijing Peoples R China

ISBN: (纸本)9781509040322

In this paper, we propose a subspace method for solving unconstrained optimization problems without derivatives. In each iteration, we construct a subspace, which enables a large-scale unconstrained optimization problem to be transformed into a lower dimensional subproblem. This paper describes how to use polynomial interpolation model to capture the information of function and its derivatives, and introduces two kinds of subspace algorithms of different dimensions without derivatives. The new algorithm not only has less computational complexity, but also can be applied to the problem that the derivative information is difficult to obtain or even can not be completely solved.

关键词： unconstrained optimization problem without derivative subspace numerical comparisons

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ALGORITHMS FOR SOLVING unconstrained optimization problemS 12

ALGORITHMS FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS

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12th International Computer Conference on Wavelet Active Media Technology and Information Processing (ICCWAMTIP)

作者： Kuang, Ping Zhao, Qin-Min Xie, Zhen-Yu Univ Elect Sci & Technol China Sch Informat & Software Engn Chengdu 611731 Peoples R China

ISBN: (纸本)9781467382663

The computational method of unconstrained optimization problem is an important research topic in the field of numerical computation. It is of great significance to solve the problem of unconstrained optimization. There are many ways that are applied to settle these questions, so we need to choose a method which owns much fast er and less complex trait. Furthermore, in order to solve this rubs, this paper presents a comparative study of the common algorithms and our approach which are used to handle some concrete unconstrained optimization problems.

关键词： unconstrained optimization problem algorithm optimization optimization method

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GPGPU based Teaching Learning based optimization and Artificial Bee Colony Algorithm for unconstrained optimization problems 5

GPGPU based Teaching Learning based Optimization and Artific...

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IEEE International Advance Computing Conference (IACC 2015)

作者： Mane, Sandeep U. Omane, Rajshree Pawar, Aprupa Rajarambapu Inst Technol Dept CSE Rajaramnagar India

ISBN: (纸本)9781479980475

Teaching learning based optimization (TLBO) and Artificial bee colony (ABC) algorithm is population based modern method of optimization, used to solve diverse complex engineering and real time applications. To obtain best solution for the complex problem it requires more time and results in performance degradation. To improve the performance of the population based algorithm, they are either parallelized or implemented on General Purpose Graphic Processing Unit (GPGPU). In this paper, the GPGPU based implementation of TLBO and ABC algorithm is discussed to solve unconstrained benchmark problems. The performance of both the approaches is compared based on standard deviation, standard error mean and time. It is observed that both the approaches gives good results but time taken by TLBO algorithm is more as compared to ABC algorithm.

关键词： Artificial bee colony Teaching learning based optimization unconstrained optimization problem General Purpose Graphic Processing Unit

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Low-complexity linear massive MIMO detection based on the improved BFGS method

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IET COMMUNICATIONS 2022年第14期16卷 1699-1707页

作者： Li, Lin Hu, Jianhao Univ Elect Sci & Technol China Chengdu Sichuan Peoples R China Qinghai Normal Univ Xining Qinghai Peoples R China

Linear minimum mean square error (MMSE) detection achieves a good trade-off between performance and complexity for massive multiple-input multiple-output (MIMO) systems. To avoid the high-dimensional matrix inversion involved, MMSE detection can be transformed into an unconstrained optimization problem and then solved by efficient numerical algorithms in an iterative way. Three low-complexity Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton methods are proposed to iteratively realize massive MIMO MMSE detection without matrix inversion. The complexity can be reduced from O(K3)$\mathcal {O}(K<^>{3})$ to O(LK2)$\mathcal {O}(LK<^>{2})$, where K and L denote the number of users and iterations, respectively. Leveraging the special properties of massive MIMO, the authors first explore a simplified BFGS method (named S-BFGS) to alleviate the computational burden in the search direction. For lower complexity, BFGS method with the unit step size (named U-BFGS) is presented subsequently. When the base station (BS)-to-user-antenna ratio (BUAR) is large enough, the two proposed BFGS methods can be integrated (named U-S-BFGS) to further reduce complexity. In addition, an efficient initialization strategy is devised to accelerate convergence. Simulation results verify that the proposed detection scheme can achieve near-MMSE performance with a small number of iterations L as low as 2 or 3.

关键词： base station-to-user-antenna ratio MIMO communication matrix inversion least mean squares methods optimisation linear minimum mean square error detection simplified BFGS method computational complexity massive MIMO MMSE detection Newton method high-dimensional matrix inversion low-complexity Broyden-Fletcher-Goldfarb-Shanno quasiNewton methods detection scheme improved BFGS method near-MMSE performance iterative methods U-BFGS convergence of numerical methods maximum likelihood detection unconstrained optimization problem low-complexity linear massive MIMO detection massive multiple-input multiple-output systems

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