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stochastic Primal Dual Fixed Point Method for Composite Optimization

JOURNAL OF SCIENTIFIC COMPUTING 2020年第1期84卷 16-16页

作者： Zhu, Ya-Nan Zhang, Xiaoqun Shanghai Jiao Tong Univ Inst Nat Sci Sch Math Sci Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ MOE LSC Shanghai 200240 Peoples R China

In this paper we propose a stochastic primal dual fixed point method for solving the sum of two proper lower semi-continuous convex function and one of which is composite. The method is based on the primal dual fixed point method proposed in Chen et al. (Inverse Probl 29:025011, 2013) that does not require subproblem solving. Under some mild condition, the convergence is established based on two sets of assumptions: bounded and unbounded gradients and the convergence rate of the expected error of iterate is of the order O(k(-alpha)) where k is iteration number and alpha is an element of (0, 1]. Finally, numerical examples on graphic Lasso and logistic regressions are given to demonstrate the effectiveness of the proposed algorithm.

关键词： stochastic algorithm Proximal point method Primal dual Fixed point Composite optimization Graphic lasso

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The Battery Life Estimation of a Battery under Different Stress Conditions

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BATTERIES-BASEL 2021年第4期7卷 88页

作者： Andrenacci, Natascia Vellucci, Francesco Sglavo, Vincenzo CR ENEA Casaccia Via Anguillarese 301 I-00123 Rome Italy

The prediction of capacity degradation, and more generally of the behaviors related to battery aging, is useful in the design and use phases of a battery to help improve the efficiency and reliability of energy systems. In this paper, a stochastic model for the prediction of battery cell degradation is presented. The proposed model takes its cue from an approach based on Markov chains, although it is not comparable to a Markov process, as the transition probabilities vary with the number of cycles that the cell has performed. The proposed model can reproduce the abrupt decrease in the capacity that occurs near the end of life condition (80% of the nominal value of the capacity) for the cells analyzed. Furthermore, we illustrate the ability of this model to predict the capacity trend for a lithium-ion cell with nickel manganese cobalt (NMC) at the cathode and graphite at the anode, subjected to a life cycle in which there are different aging factors, using the results obtained for cells subjected to single aging factors.

关键词： cycle aging lithium battery stochastic algorithm

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Uniform-in-time estimates for mean-field type SDEs and applications

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Journal of Differential Equations 2025年 440卷

作者： Bao, Jianhai Hao, Jiaqing Center for Applied Mathematics Tianjin University Tianjin 300072 China

Via constructing an asymptotic coupling by reflection, in this paper we establish uniform-in-time estimates on probability distributions for mean-field type SDEs, where the drift terms under consideration are dissipative merely in the long distance. As applications, we (i) explore the long time estimate on probability distributions associated with an SDE and its delay version;(ii) investigate the issue on uniform-in-time propagation of chaos for McKean-Vlasov SDEs, where the drifts might be singular with respect to the spatial variables;(iii) tackle the discretization error bounds in an infinite-time horizon for stochastic algorithms (e.g. backward/tamed/adaptive Euler-Maruyama schemes as three typical candidates) associated with McKean-Vlasov SDEs. © 2025 Elsevier Inc.

关键词： Asymptotic coupling by reflection Mean-field type SDE Propagation of chaos stochastic algorithm Uniform-in-time estimate

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Non-convex multiobjective optimization under uncertainty: a descent algorithm. Application to sandwich plate design and reliability

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ENGINEERING OPTIMIZATION 2019年第5期51卷 733-752页

作者： Mercier, Q. Poirion, F. Desideri, J. A. Off Natl Etud & Rech Aerosp Chatillon France INRIA Nice France

In this paper a novel algorithm for solving multiobjective design optimization problems with non-smooth objective functions and uncertain parameters is presented. The algorithm is based on the existence of a common descent vector for each sample of the random objective functions and on an extension of the stochastic gradient algorithm. The proposed algorithm is applied to the optimal design of sandwich material. Comparisons with the genetic algorithm NSGA-II and the DMS solver are given and show that it is numerically more efficient due to the fact that it does not necessitate the objective function expectation evaluation. It can moreover be entirely parallelizable. Another simple illustration highlights its potential for solving general reliability problems, replacing each probability constraint by a new objective written in terms of an expectation. Moreover, for this last application, the proposed algorithm does not necessitate the computation of the (small) probability of failure.

关键词： Multiobjective optimization uncertainty stochastic algorithm reliability

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Joint Optimization on Both Routing and Resource Allocation for Millimeter Wave Cellular Networks

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IEEE ACCESS 2019年 7卷 93631-93642页

作者： Ji, Pengshuo Jia, Jie Chen, Jian Northeastern Univ Dept Comp Sci & Engn Shenyang 110819 Liaoning Peoples R China Minist Educ Engn Res Ctr Secur Technol Complex Network Syst Shenyang 110819 Liaoning Peoples R China Southeast Univ Key Lab Comp Network & Informat Integrat Minist Educ Nanjing 211189 Jiangsu Peoples R China Liaoning Res Ctr Safety Engn Technol Ind Control Neusoft Grp Res Shenyang 110179 Liaoning Peoples R China

Due to the spectrum scarcity issue in conventional cellular networks, millimeter-wave ( mmWave) technology has been proposed and is expected to be used in small cells to meet the requirements for spectrum resources, especially for those small cells that are densely deployed and form a multi-hop backhaul structure. For this novel architecture, a cross-layer optimization problem aiming at maximizing the energy efficiency while taking into account both the route selection and resource allocation is formulated. To find the optimal solution, we first decouple the original problem into a resource allocation sub-problem at the link-physical layer and a route selection sub-problem at the network layer. Since the resource allocation sub-problem at the link-physical layer is a non-convex problem and NP-hard, we apply stochastic algorithms to search for the optimal solution. Since the network layer sub-problem is simplified as a linear programming problem, an LP solver is applied to optimize energy efficiency. To reflect the interplay between these two problems, we further propose two joint optimization strategies. One uses stochastic algorithms that are composed of four schemes with given routes for resource allocation and linear programming for the route selection based on the given resource allocation. The other uses the linear programming to evaluate the fitness of each individual in the stochastic algorithms. The simulation results reveal the following: 1) our proposed schemes are capable of finding near-optimal solutions and can improve the energy and spectrum efficiency;and 2) properly finding the route without overloading any one of the base stations is capable of improving the throughput of the networks.

关键词： Cross-layer optimization mmWave resource allocation route selection stochastic algorithm

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Multi-Scale Quantum Harmonic Oscillator algorithm With Truncated Mean Stabilization Strategy for Global Numerical Optimization Problems

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IEEE ACCESS 2019年 7卷 18926-18939页

作者： Ye, Xinggui Wang, Peng Xin, Gang Jin, Jin Huang, Yan Univ Chinese Acad Sci Beijing 100049 Peoples R China Chinese Acad Sci Chengdu Inst Comp Applicat Chengdu 610041 Sichuan Peoples R China China Unicom Cloud Comp & Big Data Ctr Fujian Branch Fuzhou 350007 Fujian Peoples R China Southwest Minzu Univ Sch Comp Sci & Technol Chengdu 610225 Sichuan Peoples R China Huaiyin Normal Univ Sch Comp Sci & Technol Huaian 223300 Peoples R China

A multi-scale quantum harmonic oscillator algorithm (MQHOA) is a quantum population-based algorithm proposed recently. It utilizes the quantum wave function to locate the global optimum of a global numerical optimization problem. As the MQHOA employs the elitism to replace the worst particle in each iteration cycle, it reduces one of the particles in each run, which will cripple the diversity of the population and slow down the convergence speed. Therefore, the particles will be easily trapped into local optima. In this paper, we suggest a new MQHOA with truncated mean stabilization (TS-MQHOA) policy to alleviate the above-mentioned problems. The theoretical and experimental analyses indicate that the truncated mean stabilization strategy helps to diversify the populations and improve the convergence efficiency. The proposed TS-MQHOA is evaluated on a number of dimensionwise unimodal and multimodal CEC benchmark functions, and the computational results are compared with several popular population-based algorithms. The experimental results on complex test problems demonstrate that the proposed TS-MQHOA, in most function evaluations, is able to obtain better convergence toward the global optimum compared with several renowned heuristic algorithms based on swarm intelligence. Meanwhile, the comparative results reveal the competitiveness and superiority of the proposed algorithm, especially on high-dimensional function evaluations.

关键词： Multi-scale quantum harmonic oscillator algorithm swarm intelligence population-based algorithm stochastic algorithm truncated mean stabilization strategy

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Optimization of Microalgae-to-Biodiesel Production Process Using a Metaheuristic Technique

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ACS SUSTAINABLE CHEMISTRY & ENGINEERING 2019年第9期7卷 8490-8498页

作者： German Hernandez-Perez, Luis Sanchez-Tuiran, Eduardo Ojeda, Karina A. E-Halwagi, Mahmoud M. Ponce-Ortega, Jose M. Univ Michoacana Chem Engn Dept Francisco J Mujica S-NCiudad Univ Morelia 58060 Michoacan Mexico Univ Cartagena Chem Engn Dept Av ConsuladoCalle 3039B-192 Cartagena De Indias 130015 Colombia Texas A&M Univ Chem Engn Dept 100 Spence StJack E Brown Bldg College Stn TX 77843 USA

This paper presents an effective computational scheme using metaheuristic techniques for the optimization of an integrated biodiesel production process from microalgae Chlorella vulgaris. Ten decision variables were optimized including temperatures and pressures of the five process reactors and the number of stages and feed stage of the three considered distillation columns. The model is a multiobjective formulation involving economic and environmental objectives. The economic objective function is aimed at maximizing the total annual income. The objective function associated with the environmental impact is to minimize the produced greenhouse gases. Process data were obtained from the simulation software Aspen Plus. Models for determining the properties for new substances missing in the database, such as fatty acids present in the microalgae, were considered to improve the predictions of the raw material properties. The free software Symyx Draw was used for the creation of all the components that were not in the Aspen Plus database. The optimization tool that was used in this paper consists of a stochastic algorithm called I-MODE (improved multiobjective differential evolution). Likewise, a linking subroutine based on COM (component object module) technology and developed in Excel-Visual Basic for Applications scripts was implemented to control the Aspen Plus software for various sets of decision variables. The results offer attractive options for both economic and environmental benefits.

关键词： Multiobjective optimization Optimal design Biodiesel production process Microalgae stochastic algorithm

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AtomREM: Non-empirical seeker of the minimum energy escape paths on many-dimensional potential landscapes without coarse graining

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COMPUTER PHYSICS COMMUNICATIONS 2020年 254卷 107260-107260页

作者： Nagornov, Yuri S. Akashi, Ryosuke Univ Tokyo Dept Phys Bunkyo Ku Tokyo 1130033 Japan

Recently a non-empirical stochastic walker algorithm has been developed to search for the minimum-energy escape paths from the minima of the potential surface (Akashi and Nagornov, 2018;Nagornov and Akashi, 2019). This method is based on the Master equation for the distribution function of the atomic configuration which has a nature to seek the reaction path up along the valley of the potential surface. This paper introduces AtomREM (Atomistic Rare Event Manager), which is an MPI parallelized solver program package for executing this method, which yields reaction pathways in terms of the microscopic evolution of atomic positions. It is open-source and released under the GNU General Public License (GPL). A feature AtomREM interfaces with the LAMMPS Molecular Dynamics Simulator as a library of versatile potential functions for application to various systems. Examples of the applications to molecular and solid systems are presented. Program summary Program Title: AtomREM (Atomistic Rare-Event Manager) Program Files doi: http://***/10.17632/ys5mpgjfc8.1 Licensing provisions: GNU General Public License 3 Programming language: Fortran 90 and C Supplementary material: Result movies of simulation for argon solid and (CH2)(4) molecule Nature of problem: AtomREM has been developed to help to find a reaction path on the atomic level using weighted Langevin mechanics on the inverse potential landscape. The method describes the low temperature transformation of complex systems without artificial forces or/and collective variables. Solution method: Recently [1] we designed a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby with one dimensional application. The method is based on the Master equation and its solver algorithm is constructed to move the walkers up the surface through the potential valleys [2]. The stochastic algorithm uses a birth/death stochastic processes for numerous

关键词： Potential landscape Reaction paths Minimum-energy escape paths Langevin mechanics Non-empirical scheme stochastic algorithm Parallel MPI implementation

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Balancing exploration and exploitation: An image-based approach to item retrieval with enhanced diversity

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COMPUTERS & ELECTRICAL ENGINEERING 2020年 84卷 106605-106605页

作者： Pereira, Artur Maia Vieira, Thales Costa, Evandro de Barros Univ Fed Alagoas Inst Comp Maceio Alagoas Brazil Univ Fed Alagoas Inst Math Maceio Alagoas Brazil

We propose a machine learning approach based on relevance feedback to visually retrieve e-commerce items, represented by images, from huge catalogs. A threefold strategy is presented to deal with the exploration-exploitation dilemma: retrieve user-relevant items;retrieve items that do not comply with user learned preferences, to avoid convergence to local minima;and retrieve items from uncertainty regions, to improve the learning curve, all in a stochastic manner. To mitigate the cold start problem, we present a novel sampling method to improve the diversity of retrieved items that employs a combination of a multidimensional projection method with an adaptive spatial data structure. We performed quantitative and qualitative user experiments using an annotated catalog of clothing items. Results revealed that our approach can rapidly improve the retrieval of appropriate items in a few user iterations while providing higher diversity than other relevant and recent approaches. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Concept-based retrieval Relevance feedback Dimensionality reduction stochastic algorithm Exploration-exploitation Item retrieval

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A general scheme for log-determinant computation of matrices via stochastic polynomial approximation

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2018年第4期75卷 1259-1271页

作者： Peng, Wei Wang, Hongxia Natl Univ Def Technol Dept Math & Syst Sci Changsha 410073 Hunan Peoples R China

We study the approximation of determinant for large scale matrices with low computational complexity. This paper develops a generalized stochastic polynomial approximation frame as well as a stochastic Legendre approximation algorithm to calculate log-determinants of large-scale positive definite matrices based on the prior eigenvalue distributions. The generalized frame is implemented by weighted L-2 orthogonal polynomial expansions with an efficient recursion formula and matrix-vector multiplications. So the proposed scheme is efficient both in computational complexity and data storage. Respective error bounds are given in theory which guarantee the convergence of the proposed algorithms. We illustrate the effectiveness of our method by numerical experiments on both synthetic matrices and counting spanning trees. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Log-determinant Orthogonal polynomial expansions stochastic algorithm Counting spanning trees

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