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lipschitz optimization for phase stability analysis: application to Soave-Redlich-Kwong equation of state

FLUID PHASE EQUILIBRIA 1999年第1-2期162卷 19-29页

作者： Zhu, YS Xu, ZH Chinese Acad Sci Lab Comp Chem Inst Chem Met Beijing 100080 Peoples R China

The Gibbs tangent plane analysis is the crucial method for the determination of the global phase stability and the true equilibrium compositions of the system at elevated pressures. Previous approaches have focused on finding stationary points of the tangent plane distance function (TPDF) described by the cubic equation of state. However, there is no complete guarantee of obtaining all stationary points due to the nonconvex and nonlinear nature of the models used to predict high pressure phase equilibria. After analyzing and reformulating the structure of the derivative function of the TPDF described by the Soave-Redlich-Kwong (SRK) equation of state, it was demonstrated that the lipschitz constant of the TPDF can be obtained with the calculation precision satisfied. Then the phase stability problem can be solved with E-global convergence. The calculation results for two examples state that the lipschitz optimization algorithm, i.e., Piyavskii's univariate lipschitz optimization algorithm used in this paper, can obtain the global minimum of the TPDF for binary mixtures at elevated pressures with complete reliability. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： tangent plane analysis high pressure phase equilibria lipschitz optimization TPDF Gibbs free energy

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Accelerate Neural Subspace-Based Reduced-Order Solver of Deformable Simulation by lipschitz optimization

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ACM TRANSACTIONS ON GRAPHICS 2024年第6期43卷 1-10页

作者： Lyu, Aoran Zhao, Shixian Xian, Chuhua Cen, Zhihao Cai, Hongmin Fang, Guoxin South China Univ Technol Guangzhou Peoples R China Univ Manchester Manchester England Chinese Univ Hong Kong Hong Kong Peoples R China

Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more concise subspaces can be detected. However, the complexity and landscape of simulation objectives within the subspace have not been optimized, which leaves room for enhancement of the convergence speed. This work focuses on this point by proposing a general method for finding optimized subspace mappings, enabling further acceleration of neural reduced-order simulations while capturing comprehensive representations of the configuration manifolds. We achieve this by optimizing the lipschitz energy of the elasticity term in the simulation objective, and incorporating the cubature approximation into the training process to manage the high memory and time demands associated with optimizing the newly introduced energy. Our method is versatile and applicable to both supervised and unsupervised settings for optimizing the parameterizations of the configuration manifolds. We demonstrate the effectiveness of our approach through general cases in both quasi-static and dynamics simulations. Our method achieves acceleration factors of up to 6.83 while consistently preserving comparable simulation accuracy in various cases, including large twisting, bending, and rotational deformations with collision handling. This novel approach offers significant potential for accelerating physical simulations, and can be a good add-on to existing neural-network-based solutions in modeling complex deformable objects.

关键词： Deformable Simulation Model Reduction Neural Subspace Detection lipschitz optimization

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NEW LP BOUND IN MULTIVARIATE lipschitz optimization - THEORY AND APPLICATIONS

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JOURNAL OF optimization THEORY AND APPLICATIONS 1995年第2期86卷 369-388页

作者： HORST, R NAST, M THOAI, NV INST MATH HANOIVIETNAM

Most numerically promising methods for solving multivariate unconstrained lipschitz optimization problems of dimension greater than two use rectangular or simplicial branch-and-bound techniques with computationally cheap but rather crude lower bounds. Generalizations to constrained problems, however, require additional devices to detect sufficiently many infeasible partition sets. In this article, a new lower bounding procedure is proposed methods yielding considerably better bounds at the expense of two linear programs in each iteration. Moreover, the resulting approach can solve easily linearly constrained problems, since in this case infeasible partition sets are automatically detected by the lower bounding procedure. Finally, it is shown that the lower bounds can be further improved when the method is applied to solve systems of inequalities. Implementation issues, numerical experiments, and comparisons are discussed in some detail.

关键词： GLOBAL optimization lipschitz optimization SYSTEMS OF INEQUALITIES BRANCH-AND-BOUNDS METHODS

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An algorithm of simplicial lipschitz optimization with the bi-criteria selection of simplices for the bi-section

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JOURNAL OF GLOBAL optimization 2018年第1期71卷 115-127页

作者： Gimbutas, Albertas Zilinskas, Antanas Vilnius Univ Inst Math & Informat Akad 4 LT-08663 Vilnius Lithuania

An algorithm of simplicial optimization is proposed where a bi-criteria selection of a simplex for the bi-section is applied. The first criterion is the minimum of estimated lipschitz lower bound over the considered s... 详细信息

关键词： lipschitz optimization Global optimization Simplicial partition Multicriteria selection

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Simplicial lipschitz optimization without the lipschitz constant

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JOURNAL OF GLOBAL optimization 2014年第1期59卷 23-40页

作者： Paulavicius, Remigijus Zilinskas, Julius Vilnius State Univ Inst Math & Informat LT-08663 Vilnius Lithuania

In this paper we propose a new simplicial partition-based deterministic algorithm for global optimization of lipschitz-continuous functions without requiring any knowledge of the lipschitz constant. Our algorithm is motivated by the well-known Direct algorithm which evaluates the objective function on a set of points that tries to cover the most promising subregions of the feasible region. Almost all previous modifications of Direct algorithm use hyper-rectangular partitions. However, other types of partitions may be more suitable for some optimization problems. Simplicial partitions may be preferable when the initial feasible region is either already a simplex or may be covered by one or a manageable number of simplices. Therefore in this paper we propose and investigate simplicial versions of the partition-based algorithm. In the case of simplicial partitions, definition of potentially optimal subregion cannot be the same as in the rectangular version. In this paper we propose and investigate two definitions of potentially optimal simplices: one involves function values at the vertices of the simplex and another uses function value at the centroid of the simplex. We use experimental investigation to compare performance of the algorithms with different definitions of potentially optimal partitions. The experimental investigation shows, that proposed simplicial algorithm gives very competitive results to Direct algorithm using standard test problems and performs particularly well when the search space and the numbers of local and global optimizers may be reduced by taking into account symmetries of the objective function.

关键词： Global optimization lipschitz optimization Simplicial Direct-type algorithm Potentially optimal simplex

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Adaptation of a one-step worst-case optimal univariate algorithm of bi-objective lipschitz optimization to multidimensional problems

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2015年第1-3期21卷 89-98页

作者： Zilinskas, Antanas Zilinskas, Julius Vilnius Univ Inst Math & Informat LT-08663 Vilnius Lithuania

A bi-objective optimization problem with lipschitz objective functions is considered. An algorithm is developed adapting a univariate one-step optimal algorithm to multidimensional problems. The univariate algorithm considered is a worst-case optimal algorithm for lipschitz functions. The multidimensional algorithm is based on the branch-and-bound approach and trisection of hyper-rectangles which cover the feasible region. The univariate algorithm is used to compute the lipschitz bounds for the Pareto front. Some numerical examples are included. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Multi-objective optimization Optimal algorithms Global optimization lipschitz optimization

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On one-step worst-case optimal trisection in univariate bi-objective lipschitz optimization

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COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION 2016年 35卷 123-136页

作者： Zilinskas, Antanas Gimbutiene, Grazina Vilnius State Univ Inst Math & Informat LT-08663 Vilnius Lithuania

The bi-objective lipschitz optimization with univariate objectives is considered. The concept of the tolerance of the lower lipschitz bound over an interval is generalized to arbitrary subintervals of the search region. The one-step worst-case optimality of trisecting an interval with respect to the resulting tolerance is established. The theoretical investigation supports the previous usage of trisection in other algorithms. The trisection-based algorithm is introduced. Some numerical examples illustrating the performance of the algorithm are provided. (C) 2015 Elsevier B.V. All rights reserved.

关键词： Bi-objective optimization Optimal algorithms lipschitz optimization Trisection

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Dual and bidual problems for a lipschitz optimization problem based on quasi-conjugation

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2011年第1期378卷 198-212页

作者： Yamada, Syuuji Tanaka, Tamaki Tanino, Tetsuzo Niigata Univ Grad Sch Sci & Technol Niigata 9502181 Japan Osaka Univ Grad Sch Engn Suita Osaka 5650871 Japan

In this paper, we consider a lipschitz optimization problem (LOP) constrained by linear functions in R(n). In general, since it is hard to solve (LOP) directly. (LOP) is transformed into a certain problem (MP) constrained by a ball in R(n+1). Despite there is no guarantee that the objective function of (MP) is quasi-convex, by using the idea of the quasi-conjugate function defined by Thach (1991) [1], we can construct its dual problem (DP) as a quasi-convex maximization problem. We show that the optimal value of (DP) coincides with the multiplication of the optimal value of (MP) by -1. and that each optimal solution of the primal and dual problems can be easily obtained by the other. Moreover, we formulate a bidual problem (BDP) for (MP) (that is, a dual problem for (DP)). We show that the objective function of (BDP) is a quasi-convex function majorized by the objective function of (MP) and that both optimal solution sets of (MP) and (BDP) coincide. Furthermore, we propose an outer approximation method for solving (DP). (C) 2010 Elsevier Inc. All rights reserved.

关键词： lipschitz optimization Duality Quasi-conjugate function Outer approximation method

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Peer-to-peer Estimation over Wireless Sensor Networks via lipschitz optimization

Peer-to-peer Estimation over Wireless Sensor Networks via Li...

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8th International Symposium on Information Processing Sensor Networks

作者： Fischione, Carlo Speranzon, Alberto Johansson, Karl Henrik Sangiovanni-Vincentelli, Alberto Royal Inst Technol ACCESS Linnaeus Ctr S-10044 Stockholm Sweden United Technol Res Ctr E Hartford CT 06108 USA Univ Calif Berkeley Berkeley CA 94720 USA

ISBN: (纸本)9781424451081

Motivated by a peer-to-peer estimation algorithm in which adaptive weights are optimized to minimize the estimation error variance, we formulate and solve a novel non-convex lipschitz optimization problem that guarantees global stability of a large class of peer-to-peer consensus-based algorithms for wireless sensor network. Because of packet. losses, the solution of this optimization problem cannot be achieved efficiently with either traditional centralized methods or distributed Lagrangian message passing. The prove that the optimal solution can be obtained by solving a set of nonlinear equations. A fast distributed algorithm, which requires only local computations, is presented for solving these equations. Analysis and computer simulations illustrate the algorithm and its application to various network topologies.

关键词： lipschitz optimization Parallel and Distributed Computation Wireless Sensor Networks Distributed Estimation

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Modified lipschitz optimization and its application to maximum power point tracking control for photovoltaic systems

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IEEJ TRANSACTIONS ON ELECTRICAL AND ELECTRONIC ENGINEERING 2022年第6期17卷 816-822页

作者： Masuda, Eiji Wakasa, Yuji Adachi, Ryosuke Yamaguchi Prefectural Ind Technol Inst 4-1-1 Asutopia Ube Yamaguchi 7550195 Japan Yamaguchi Univ Grad Sch Sci & Technol Innovat 2-16-1 Tokiwadai Ube Yamaguchi 7558611 Japan

In this paper, we propose a modified lipschitz optimization (LO) method and apply it to maximum power point tracking (MPPT) control for photovoltaic (PV) systems. The standard LO can find a global maximum of a lipschitz continuous function over a closed interval in a deterministic way. However, the standard LO tends to evaluate low objective function values, and this feature leads to low MPPT efficiency in its application to MPPT control. The proposed method skips the evaluation of low objective function values (i.e., low power points) by using prior information on the output characteristics of a PV array. Moreover, we show theoretically that the proposed method guarantees convergence to a global optimal solution. We compare the proposed method with some of well-known MPPT methods and verify its effectiveness through simulations. (c) 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

关键词： maximum power point tracking control partial shading condition lipschitz optimization global optimization

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