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A new nonmonotone line search technique for unconstrained optimization

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2008年第1期219卷 134-144页

作者： Yu, Zhensheng Pu, Dingguo Shanghai Univ Sci & Technol Coll Sci Shanghai 200093 Peoples R China Tongji Univ Dept Appl Math Shanghai 200092 Peoples R China

In this paper, we propose a new nonmonotone line search technique for unconstrained optimization problems. By using this new technique. we establish the global convergence under conditions weaker than those of the exi... 详细信息

关键词： unconstrained optimization problem nonmonotone F-rule global convergence memoryless quasi-Newton method

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Congestion and environmental toll schemes for the morning commute with heterogeneous users and parallel routes

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2019年 129卷 305-333页

作者： Long, Jiancheng Szeto, W. Y. Hefei Univ Technol Sch Automot & Transportat Engn Hefei 230009 Anhui Peoples R China Univ Hong Kong Dept Civil Engn Pokfulam Rd Hong Kong Peoples R China

We design a congestion and environmental toll (CET) scheme for the morning commute with heterogeneous users in a single OD network with parallel routes. The designed toll scheme relies upon the concept of marginal-cost pricing and is anonymous. The Henderson approach is used to model road congestion and the tolling problem to examine commuter's arrival time and route choice at the CET equilibrium (CETE). Linear interpolation is applied to approximate the emission cost function and the resulting CETE problem is formulated as an unconstrained optimization problem, which is solved by the modified Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. Unlike the existing approach, this novel approach does not require that the arrival of each group of commuters at the destination at the equilibrium follows a predetermined order, and can handle non-monotone (emission) cost function. As two special cases, no-toll equilibrium (NTE) and the congestion toll equilibrium (CTE) are also examined, and the two resultant equilibrium problems are formulated and solved by the same approach. This approach is shown to be more efficient than the existing approach. Bi-level programming models are proposed to formulate the optimal congestion toll and CET design problems, in which the CTE and CETE problems are the corresponding lower level problem. These models are solved by the double BFGS method, which uses a classical BFGS method to solve the upper level model and the proposed BFGS method to solve the lower level model. Finally, numerical examples are provided to illustrate the properties of the models and the efficiency of the proposed solution algorithms. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Air pollution BFGS method General heterogeneity Morning commute Road pricing unconstrained optimization problem

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Gap functions and global error bounds for set-valued variational inequalities

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2010年第11期233卷 2956-2965页

作者： Fan Jianghua Wang Xiaoguo Guangxi Normal Univ Guilin 541004 Guangxi Peoples R China

The set-valued variational inequality problem is very useful in economics theory and nonsmooth optimization. In this paper, we introduce some gap functions for set-valued variational inequality problems under suitable assumptions. By using these gap functions we derive global error bounds for the solution of the set-valued variational inequality problems. Our results not only generalize the previously known results for classical variational inequalities from single-valued case to set-valued, but also present a way to constructgap functions and derive global error bounds forset-valued variational inequality problems. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Set-valued variational inequality problem unconstrained optimization problem Gap functions Global error bounds

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An efficient new hybrid CG-method as convex combination of DY and CD and HS algorithms

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RAIRO-OPERATIONS RESEARCH 2022年第6期56卷 4047-4056页

作者： Hallal, Amina Belloufi, Mohammed Sellami, Badreddine Mohamed Cherif Messaadia Univ Dept Math & Informat Lab Informat & Math LiM Souk Ahras Algeria

In this paper, we proposed a new hybrid conjugate gradient algorithm for solving unconstrained optimization problems as a convex combination of the Dai-Yuan algorithm, conjugate-descent algorithm, and Hestenes-Stiefel algorithm. This new algorithm is globally convergent and satisfies the sufficient descent condition by using the strong Wolfe conditions. The numerical results show that the proposed nonlinear hybrid conjugate gradient algorithm is efficient and robust.

关键词： unconstrained optimization problem hybrid conjugate gradient method strong Wolfe line search sufficient descent condition

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A unifying approach to constrained and unconstrained optimal reinsurance

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2019年 360卷 1-17页

作者： Huang, Yuxia Yin, Chuancun Qufu Normal Univ Sch Stat Jining 273165 Shandong Peoples R China

In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination of the total losses where the risk is measured by a distortion risk measure and the reinsurance premium is calculated according to a distortion premium principle. In the first place, we show how to formulate the unconstrained optimization problem and constrained optimization problem in a unified way. Then, we propose a geometric approach to solve optimal reinsurance problems directly. This paper considers a class of increasing convex ceded loss functions and derives the explicit solutions of the optimal reinsurance, which can be in forms of quota-share, stop-loss, change-loss, the combination of quota-share and change-loss or the combination of change-loss and change-loss with different retentions. Finally, we consider two specific cases of the distortion risk measures: Value at Risk (VaR) and Tail Value at Risk (TVaR). (C) 2019 Elsevier B.V. All rights reserved.

关键词： Distortion risk measure Distortion premium principle Geometric approach Lagrangian dual method unconstrained optimization problem Constrained optimization problem

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An iterative calculation method for hanger tensions and the cable shape of a suspension bridge based on the catenary theory and finite element method

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ADVANCES IN STRUCTURAL ENGINEERING 2019年第7期22卷 1566-1578页

作者： Zhang, Wen-ming Li, Tao Shi, Lu-yao Liu, Zhao Qian, Kai-rui Southeast Univ Minist Educ Key Lab Concrete & Prestressed Concrete Struct Nanjing 211189 Jiangsu Peoples R China

Construction of suspension bridges and their structural analysis are challenged by the presence of elements (chains or main cables) capable of large deflections leading to a geometric nonlinearity. For an accurate prediction of the main cable geometry of a suspension bridge, an innovative iterative method is proposed in this article. In the iteration process, hanger tensions and the cable shape are, in turns, used as inputs. The cable shape is analytically predicted with an account of the pylon saddle arc effect, while finite element method is employed to calculate hanger tensions with an account of the combined effects of the cable-hanger-stiffening girder. The cable static equilibrium state is expressed by three coupled nonlinear governing equations, which are solved by their transformation into a form corresponding to the unconstrained optimization problem. The numerical test results for the hanger tensions in an existing suspension bridge were obtained by the proposed iterative method and two conventional ones, namely, the weight distribution and continuous multiple-rigid-support beam methods. The latter two reference methods produced the respective deviations of 10% and 5% for the side hangers, respectively, which resulted in significant errors in the elevations of the suspension points. To obtain more accurate hanger tensile forces, especially for the side hangers, as well as the cable shape, the iterative method proposed in this article is recommended.

关键词： cable shape hanger tensile force iterative method pylon saddle suspension bridge tangent point unconstrained optimization problem

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Adjustment of the scaling parameter of Dai-Kou type conjugate gradient methods with application to motion control

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APPLICATIONS OF MATHEMATICS 2024年第6期69卷 829-845页

作者： Akbari, Mahbube Nezhadhosein, Saeed Heydari, Aghile Payame Noor Univ Dept Math Nakhl StLashkarak Highway Tehran 193954697 Iran

We introduce a new scaling parameter for the Dai-Kou family of conjugate gradient algorithms (2013), which is one of the most numerically efficient methods for unconstrained optimization. The suggested parameter is based on eigenvalue analysis of the search direction matrix and minimizing the measure function defined by Dennis and Wolkowicz (1993). The corresponding search direction of conjugate gradient method has the sufficient descent property and the extended conjugacy condition. The global convergence of the proposed algorithm is given for both uniformly convex and general nonlinear objective functions. Also, numerical experiments on a set of test functions of the CUTER collections and the practical problem of the manipulator of robot movement control show that the proposed method is effective.

关键词： unconstrained optimization problem self-scaling memoryless BFGS conjugate gradient measure function

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ALGORITHMS FOR SOLVING unconstrained optimization problemS

ALGORITHMS FOR SOLVING UNCONSTRAINED OPTIMIZATION PROBLEMS

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International Copmputer Conference on Wavelet Active Miedia Technology and Information Processing

作者： PING KUANG QIN-MIN ZHAO ZHEN-YU XIE School of Information and Software Engineering University of Electronic Science and Technology of China Chengdu 611731

ISBN: (纸本)9781467382670

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 faster 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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Equivalent unconstrained minimization and global error bounds for variational inequality problems

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SIAM JOURNAL ON CONTROL AND optimization 1997年第1期35卷 273-284页

作者： Yamashita, N Fukushima, M Dept. of Appl. Math. and Physics Graduate School of Engineering Kyoto University Kyoto 606-01 Japan

New merit functions for variational inequality problems are constructed through the Moreau-Yosida regularization of some gap functions. The proposed merit functions constitute unconstrained optimization problems equivalent to the original variational inequality problem under suitable assumptions. Conditions are studied for those merit functions to be differentiable and for any stationary point of those those functions to be a solution of the original variational inequality problem. Moreover, those functions are shown to provide global error bounds for general variational inequality problems under the strong monotonicity assumption only.

关键词： variational inequality problem merit function unconstrained optimization problem global error bounds

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Conjugate gradient methods using value of objective function for unconstrained optimization

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optimization LETTERS 2012年第5期6卷 941-955页

作者： Iiduka, Hideaki Narushima, Yasushi Kyushu Inst Technol Network Design Res Ctr Chiyoda Ku Tokyo 1000011 Japan Fukushima Natl Coll Technol Dept Commun & Informat Sci Iwaki Fukushima 9708034 Japan

Conjugate gradient methods have been widely used as schemes to solve large-scale unconstrained optimization problems. The search directions for the conventional methods are defined by using the gradient of the objective function. This paper proposes two nonlinear conjugate gradient methods which take into account mostly information about the objective function. We prove that they converge globally and numerically compare them with conventional methods. The results show that with slight modification to the direction, one of our methods performs as well as the best conventional method employing the Hestenes-Stiefel formula.

关键词： unconstrained optimization problem Conjugate gradient method Wolfe conditions Global convergence

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