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A smoothing algorithm for two-stage portfolio model with second-order stochastic dominance constraints

COMPUTATIONAL & APPLIED MATHEMATICS 2025年第4期44卷 1-17页

作者： Shen, Feifei Yang, Liu Yuan, Jinyun Xiangtan Univ Sch Math & Computat Sci Xiangtan 411105 Hunan Peoples R China Xiangtan Univ Hunan Key Lab Computat & Simulat Sci & Engn Xiangtan 411105 Hunan Peoples R China DongGuan Univ Technol Sch Comp Sci & Technol Dongguan 523000 Guangdong Peoples R China

A numerical algorithm is proposed for solving a new two-stage portfolio optimization model with a stochastic dominance constraint on the recourse function based on a sample average approximation method. After application of sample average approximation with some assumptions, the two-stage model becomes an equivalent one-stage non-linear program with nonsmooth plus function which can be solved by smoothing technique. Then, a smoothing algorithm is proposed for solving the two-stage portfolio model. The convergence of the proposed smoothing algorithm is studied. Numerical tests illustrated that the smoothing algorithm has better performance than the linear program algorithm introduced by Dentcheva and Ruszczy & nacute;ski in the following three aspects: (i) The number of constraints in our proposed algorithm is independent on the number of samples;(ii) The smoothing algorithm can deal with the nonlinear portfolio models with nonlinear transaction cost function;(iii) The smoothing algorithm has high computational efficiency.

关键词： Two-stage portfolio optimization models Stochastic dominance Recourse function SAA method smoothing algorithm

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Predictor-corrector inexact smoothing algorithm for symmetric cone complementarity problems with Cartesian P0-property

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APPLIED NUMERICAL MATHEMATICS 2019年 143卷 146-158页

作者： Tang, Jingyong Huang, Chengdai Wang, Yongli Xinyang Normal Univ Coll Math & Stat Xinyang 464000 Peoples R China Shandong Univ Sci & Technol Coll Math & Syst Sci Qingdao 266590 Shandong Peoples R China

In this paper we consider the symmetric cone complementarity problem with Cartesian P-0-property (denoted by P-0-SCCP) which includes the well-known monotone symmetric cone complementarity problem. We propose a predictor-corrector inexact smoothing algorithm for solving the P-0-SCCP and prove that the method is globally and locally quadratically convergent under suitable assumptions. Especially, we prove that our algorithm can generate a bounded iteration sequence when the solution set of the P-0-SCCP is nonempty and bounded, or the solution set of the monotone SCCP is nonempty. Moreover, the proposed algorithm solves the linear systems in both predictor step and corrector step only approximately by using an inexact Newton method. Hence when one solves large-scale SCCPs, our algorithm can save much computation work compared to existing smoothing-type algorithms. Numerical results confirm these good theoretical properties. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Symmetric cone complementarity problem Cartesian P-0-property smoothing algorithm Inexact Newton method Quadratical convergence

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Numerical study of a smoothing algorithm for the complementarity system over the second-order cone

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COMPUTATIONAL & APPLIED MATHEMATICS 2018年第3期37卷 2845-2861页

作者： Dong, Li Tang, Jingyong Song, Xinyu Xinyang Normal Univ Sch Math & Stat Xinyang 464000 Peoples R China

This paper deals with the complementarity system over the second-order cone (denoted by CSSOC) which contains a wide class of problems. We extend a class of regularized Chen-Harker-Kanzow-Smale smoothing functions studied by Huang and Sun (Appl Math Optim 52:237-262, 2005) for the linear complementarity problem to the CSSOC. Based on this class of functions, we propose a smoothing algorithm for solving the CSSOC. Under weak assumptions, we prove that the proposed algorithm has global and local quadratic convergence. The proposed algorithm is different from existing smoothing algorithms for solving the CSSOC because it adopts a new nonmonotone line search rule. In addition, our algorithm solves a new equation reformulation of the CSSOC. Numerical experiments indicate that the proposed algorithm is quite effective.

关键词： Complementarity system over second-order cone smoothing algorithm Global convergence Quadratic convergence

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A variant nonmonotone smoothing algorithm with improved numerical results for large-scale LWCPs

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COMPUTATIONAL & APPLIED MATHEMATICS 2018年第3期37卷 3927-3936页

作者： Tang, Jingyong Xinyang Normal Univ Sch Math & Stat Xinyang 464000 Peoples R China

This paper considers the linear weighted complementarity problem (denoted by LWCP) introduced by Potra (SIAM J Optim 22:1634-1654, 2012). Based on two weighted smoothing functions, we propose a new nonmonotone smoothing algorithm for solving the LWCP and establish its global and local quadratic convergence without the strict complementarity assumption. Compared to existing nonmonotone smoothing algorithms, the proposed algorithm solves the linear system only approximately which can save the computation work when one solves large-scale LWCPs. Moreover, the nonmonotone line search technique adopted in this paper includes the usual monotone line search and some existing nonmonotone line searches as special cases. Numerical results show that our algorithm is considerably efficient for solving large-scale LWCPs.

关键词： Linear weighted complementarity problem smoothing algorithm Inexact Newton method Nonmonotone line search

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Strong convergence properties of a modified nonmonotone smoothing algorithm for the SCCP

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OPTIMIZATION LETTERS 2018年第2期12卷 411-424页

作者： Tang, Jingyong Zhou, Jinchuan Fang, Liang Xinyang Normal Univ Coll Math & Informat Sci Xinyang 464000 Peoples R China Shandong Univ Technol Sch Sci Dept Math Zibo 255049 Peoples R China Taishan Univ Coll Math & Syst Sci Tai An 271021 Shandong Peoples R China

The smoothing algorithms have been successfully applied to solve the symmetric cone complementarity problem (denoted by SCCP), which in general have the global and local superlinear/quadratic convergence if the solution set of the SCCP is nonempty and bounded. Huang, Hu and Han [Science in China Series A: Mathematics, 52: 833-848, 2009] presented a nonmonotone smoothing algorithm for solving the SCCP, whose global convergence is established by just requiring that the solution set of the SCCP is nonempty. In this paper, we propose a new nonmonotone smoothing algorithm for solving the SCCP by modifying the version of Huang-Hu-Han's algorithm. We prove that the modified nonmonotone smoothing algorithm not only is globally convergent but also has local superlinear/quadratical convergence if the solution set of the SCCP is nonempty. This convergence result is stronger than those obtained by most smoothing-type algorithms. Finally, some numerical results are reported.

关键词： Symmetric cone complementarity problem smoothing algorithm Nonmonotone line search Quadratical convergence

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A convergent smoothing algorithm for training max-min fuzzy neural networks

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NEUROCOMPUTING 2017年 260卷 404-410页

作者： Li, Long Qiao, Zhijun Liu, Yan Chen, Yuan Hengyang Normal Univ Coll Math & Stat Hengyang 421008 Peoples R China Univ Texas Rio Grande Valley Sch Math & Stat Sci Edinburg TX 78539 USA Dalian Polytech Univ Dept Appl Math Dalian 116034 Peoples R China

In this paper, a smooth function is constructed to approximate the nonsmooth output of max-min fuzzy neural networks (FNNs) and its approximation is also presented. In place of the output of max-min FNNs by its smoothing approximation function, the error function, defining the discrepancy between the actual outputs and desired outputs of max-min FNNs, becomes a continuously differentiable function. Then, a smoothing gradient decent-based algorithm with Armijo-Goldstein step size rule is formulated to train max-min FNNs. Based on the existing convergent result, the convergence of our proposed algorithm can easily be obtained. Furthermore, the proposed algorithm also provides a feasible procedure to solve fuzzy relational equations with max-min composition. Finally, some numerical examples are implemented to support our results and demonstrate that the proposed smoothing algorithm has better learning performance than other two gradient decent-based algorithms. (C) 2017 Elsevier B.V. All rights reserved.

关键词： smoothing algorithm Max-min fuzzy neural network Convergence Fuzzy relational equation

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A smoothing algorithm for finite min-max-min problems

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OPTIMIZATION LETTERS 2009年第1期3卷 49-62页

作者： Tsoukalas, Angelos Parpas, Panos Rustem, Berc Univ London Imperial Coll Sci Technol & Med Dept Comp London England

We generalize a smoothing algorithm for finite min-max to finite min-max-min problems. We apply a smoothing technique twice, once to eliminate the inner min operator and once to eliminate the max operator. In mini-max problems, where only the max operator is eliminated, the approximation function is decreasing with respect to the smoothing parameter. Such a property is convenient to establish algorithm convergence, but it does not hold when both operators are eliminated. To maintain the desired property, an additional term is added to the approximation. We establish convergence of a steepest descent algorithm and provide a numerical example.

关键词： Approximation Function smoothing Technique Minimax Problem smoothing algorithm Order Optimality Condition

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Timing synchronization using the reliability check and smoothing algorithm in the fading channels

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IEICE TRANSACTIONS ON COMMUNICATIONS 1999年第4期E82B卷 664-668页

作者： Song, HK Korea Elect Technol Inst Fac Pyungtaek Si 451860 South Korea

A timing synchronization is required in the mobile station to determine the correct transmission timing of the mobile-to-base bursts. In this letter, a timing synchronization technique using the reliability check and smoothing algorithm is proposed for the GSM receiver. The reliability check scheme extends the usefulness of this algorithm into low SNR region. And also smoothing algorithm is carried out by a first-order filter with an asymmetric step size. Simulation results show that the proposed algorithm is adequate for timing recovery of GSM modem.

关键词： timing synchronization reliability check smoothing algorithm

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A smoothing algorithm with Constant Learning Rate for Training Two Kinds of Fuzzy Neural Networks and Its Convergence

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NEURAL PROCESSING LETTERS 2020年第2期51卷 1093-1109页

作者： Li, Long Qiao, Zhijun Long, Zuqiang Hengyang Normal Univ Coll Math & Stat Hengyang 421008 Hunan Peoples R China Univ Texas Rio Grande Valley Dept Math Edinburg TX 78539 USA

In this paper, a smoothing algorithm with constant learning rate is presented for training two kinds of fuzzy neural networks (FNNs): max-product and max-min FNNs. Some weak and strong convergence results for the algorithm are provided with the error function monotonically decreasing, its gradient going to zero, and weight sequence tending to a fixed value during the iteration. Furthermore, conditions for the constant learning rate are specified to guarantee the convergence. Finally, three numerical examples are given to illustrate the feasibility and efficiency of the algorithm and to support the theoretical findings.

关键词： smoothing algorithm max-product fuzzy neural network max-min fuzzy neural network Convergence Constant learning rate

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Sensor Saturation Compensated smoothing algorithm for Inertial Sensor Based Motion Tracking

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SENSORS 2014年第5期14卷 8167-8188页

作者： Quoc Khanh Dang Suh, Young Soo Univ Ulsan Dept Elect Engn Ulsan 680749 South Korea

In this paper, a smoothing algorithm for compensating inertial sensor saturation is proposed. The sensor saturation happens when a sensor measures a value that is larger than its dynamic range. This can lead to a considerable accumulated error. To compensate the lost information in saturated sensor data, we propose a smoothing algorithm in which the saturation compensation is formulated as an optimization problem. Based on a standard smoothing algorithm with zero velocity intervals, two saturation estimation methods were proposed. Simulation and experiments prove that the proposed methods are effective in compensating the sensor saturation.

关键词： sensor saturation compensation smoothing algorithm

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