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A composite mixed finite element model for the elasto-plastic analysis of 3D structural problems

FINITE ELEMENTS IN ANALYSIS AND DESIGN 2016年 113卷 43-53页

作者： Bilotta, Antonio Garcea, Giovanni Leonetti, Leonardo Univ Calabria Dipartimento Ingn Informat Modellist Elettron & S I-87036 Cosenza Italy

The paper proposes a 3D mixed finite element and tests its performance in elasto-plastic and limit analysis problems. A composite tetrahedron mesh is assumed over the domain. Within each element the displacement field is described by a quadratic interpolation, while the stress field is represented by a piece-wise constant description by introducing a subdivision of the element into four tetrahedral regions. The assumptions for the unknown fields make the element computationally efficient and simple to implement also in existing codes. The limit and elasto-plastic analyses are formulated as a unified mathematical programming problem allowing the use of Interior Point like algorithms. A series of numerical experiments shows that the proposed finite element is locking free and has a good plastic behavior. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Mixed finite element 3D structural problems Plastic collapse analysis Elastoplasticity conic programming

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Computational aspects of column generation for nonlinear and conic optimization: classical and linearized schemes

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2023年第3期84卷 789-831页

作者： Chicoisne, Renaud Univ Clermont Auvergne Clermont Auvergne INP LIMOS 1 Rue Chebarde F-63170 Aubiere France

Solving large scale nonlinear optimization problems requires either significant computing resources or the development of specialized algorithms. For Linear programming (LP) problems, decomposition methods can take advantage of problem structure, gradually constructing the full problem by generating variables or constraints. We first present a direct adaptation of the Column Generation (CG) methodology for nonlinear optimization problems, such that when optimizing over a structured set X plus a moderate number of complicating constraints, we solve a succession of (1) restricted master problems on a smaller set S subset of X and (2) pricing problems that are Lagrangean relaxations wrt the complicating constraints. The former provides feasible solutions and feeds dual information to the latter. In turn, the pricing problem identifies a variable of interest that is then taken into account into an updated subset S' subset of X . Our approach is valid whenever the master problem has zero Lagrangean duality gap wrt to the complicating constraints, and not only when S is the convex hull of the generated variables as in CG for LPs, but also with a variety of subsets such as the conic hull, the linear span, and a special variable aggregation set. We discuss how the structure of S and its update mechanism influence the number of iterations required to reach near-optimality and the difficulty of solving the restricted master problems, and present linearized schemes that alleviate the computational burden of solving the pricing problem. We test our methods on synthetic portfolio optimization instances with up to 5 million variables including nonlinear objective functions and second order cone constraints. We show that some CGs with linearized pricing are 2-3 times faster than solving the complete problem directly and are able to provide solutions within 1% of optimality in 6 h for the larger instances, whereas solving the complete problem runs out of memory.

关键词： Nonlinear optimization conic programming Column generation Lagrangean duality Portfolio optimization

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Full Stability in Finite-Dimensional Optimization

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MATHEMATICS OF OPERATIONS RESEARCH 2015年第1期40卷 226-252页

作者： Mordukhovich, B. S. Nghia, T. T. A. Rockafellar, R. T. Wayne State Univ Dept Math Detroit MI 48202 USA King Fahd Univ Petr & Minerals Dhahran 31261 Saudi Arabia Oakland Univ Dept Math & Stat Rochester MI 48309 USA Univ Washington Dept Math Seattle WA 98195 USA

The paper is devoted to full stability of optimal solutions in general settings of finite-dimensional optimization with applications to particular models of constrained optimization problems, including those of conic and specifically semidefinite programming. Developing a new technique of variational analysis and generalized differentiation, we derive second-order characterizations of full stability, in both Lipschitzian and Holderian settings, and establish their relationships with the conventional notions of strong regularity and strong stability for a large class of problems of constrained optimization with twice continuously differentiable data.

关键词： constrained optimization full stability variational analysis generalized differentiation conic programming semidefinite programming strong regularity strong stability

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Numerical limit analysis bounds for ductile porous media with oblate voids

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MECHANICS RESEARCH COMMUNICATIONS 2011年第5期38卷 350-354页

作者： Pastor, F. Kondo, D. Pastor, J. UPMC CNRS UMR 7190 Inst DAlembert F-75252 Paris France CNRS UMR 8107 LML F-59655 Villeneuve Dascq France Univ Savoie POLYTECHAnnecy Chambery Lab LOCIE F-73376 Le Bourget Du Lac France

The paper is devoted to a numerical limit analysis of a hollow spheroidal model with a von Mises solid matrix. To this purpose, existing kinematic and static 3D-FEM codes for the case of spherical cavities have been modified and improved to account for the model of a spheroidal cavity confocal with the external spheroidal boundary. The optimized conic programming formulations and the resulting codes appear to be very efficient. This framework is then applied to the derivation of numerical upper and lower anisotropic bounds in the case of an oblate void. The numerical results obtained from a series of tests are presented and allow to assess the accuracy of closed-form expressions of the macroscopic criteria proposed by Gologanu et al. (1994, 1997) for porous media with oblate voids. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Gurson-type models Spheroidal voids Micromechanics Limit analysis Upper and lower bounds conic programming

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A New Scheme for Guaranteed State Estimation of Power System

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IEEE TRANSACTIONS ON POWER SYSTEMS 2013年第4期28卷 4875-4876页

作者： Wang, Bin He, Guangyu Liu, Kaicheng Tsinghua Univ Beijing 100084 Peoples R China Shanghai Jiao Tong Univ Shanghai 200030 Peoples R China

Recent research has shown that the uncertainty intervals of state variables and measurements can be estimated by solving mathematical programming problems corresponding to the maximization or minimization of a component of these variables. However, the results are not guaranteed since the optimal problems are non-convex and the global optimal solutions cannot always be obtained. This paper presents a new scheme for guaranteed state estimation. Firstly, a conic programming is formulated to model these optimal problems by redefining variables and loosing the feasible space. Secondly, interval constraints propagation with all constraints concerned is applied to contract the solutions further to eliminate the pessimism. Comparisons are carried out, and results show that the result intervals are guaranteed and small enough for the control system with control dead zone concerned.

关键词： conic programming guaranteed state estimation interval constraints propagation

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CVXPY: A Python-Embedded Modeling Language for Convex Optimization

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JOURNAL OF MACHINE LEARNING RESEARCH 2016年第1期17卷 2909-2913页

作者： Diamond, Steven Boyd, Stephen Stanford Univ Dept Comp Sci Stanford CA 94305 USA Stanford Univ Dept Elect Engn Stanford CA 94305 USA

CVXPY is a domain-specific language for convex optimization embedded in Python. It allows the user to express convex optimization problems in a natural syntax that follows the math, rather than in the restrictive standard form required by solvers. CVXPY makes it easy to combine convex optimization with high-level features of Python such as parallelism and object-oriented design. CVXPY is available at *** under the GPL license, along with documentation and examples.

关键词： convex optimization domain-specific languages Python conic programming convexity verification

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Cognitive Resource Allocation for Target Tracking in Location-Aware Radar Networks

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IEEE SIGNAL PROCESSING LETTERS 2020年 27卷 650-654页

作者： Liu, Xinghua Xu, Zhenhai Dong, Wei Wang, Luoshengbin Li, Xiangyang Acad Mil Sci Informat Res Ctr Mil Sci Beijing 100142 Peoples R China Natl Univ Def Technol Changsha 410073 Peoples R China

In this letter, a general framework of cognitive resource allocation for target tracking in radar networks is proposed. Firstly, an allocation strategy evaluation metric is established in this framework, i.e., the predicted conditional Cramer-Rao lower bound (PC-CRLB), for evaluating the future response of each candidate allocation strategy. Then, the optimal resource allocation strategy can be found by solving a constrained optimization problem. To specify the framework implementation details, a dwell time allocation problem is considered. For this given problem, the analytical expressions of PC-CRLB and its derived scalar strategy evaluation metric are derived, enabling us to convert the allocation problem to a second-order cone program (SOCP). Numerical results demonstrate the effectiveness of the proposed framework.

关键词： Resource management Radar tracking Radar cross-sections Target tracking Cognitive resource allocation conic programming radar networks target tracking

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Representing quadratically constrained quadratic programs as generalized copositive programs

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OPERATIONS RESEARCH LETTERS 2012年第3期40卷 203-206页

作者： Burer, Samuel Dong, Hongbo Univ Wisconsin Wisconsin Inst Discovery Madison WI 53715 USA Univ Iowa Dept Management Sci Iowa City IA 52242 USA

We show that any (nonconvex) quadratically constrained quadratic program (QCQP) can be represented as a generalized copositive program. In fact, we provide two representations: one based on the concept of completely positive (CP) matrices over second-order cones, and one based on CP matrices over the positive semidefinite cone. (C) 2012 Elsevier B.V. All rights reserved.

关键词： conic programming Copositive programming Quadratically constrained quadratic programs

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A semi-smooth Newton method for projection equations and linear complementarity problems with respect to the second order cone

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LINEAR ALGEBRA AND ITS APPLICATIONS 2017年 513卷 160-181页

作者： Cruz, J. Y. Bello Ferreira, O. P. Nemeth, S. Z. Prudente, L. F. Northern Illinois Univ Dept Math Sci WH 366 De Kalb IL 60115 USA Univ Fed Goias IME Ave Esperanga S-NCampus Samambaia BR-74690900 Goiania Go Brazil Univ Birmingham Sch Math Watson Bldg Birmingham B15 2TT W Midlands England

In this paper a special semi-smooth equation associated to the second order cone is studied. It is shown that, under mild assumptions, the semi-smooth Newton method applied to this equation is well-defined and the generated sequence is globally and Q-linearly convergent to a solution. As an application, the obtained results are used to study the linear second order cone complementarity problem, with special emphasis on the particular case of positive definite matrices. Moreover, some computational experiments designed to investigate the practical viability of the method are presented. (C) 2016 Published by Elsevier Inc.

关键词： Semi-smooth system conic programming Second order cone Semi-smooth Newton method

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CONSTRAINT QUALIFICATIONS FOR EXTENDED FARKAS'S LEMMAS AND LAGRANGIAN DUALITIES IN CONVEX INFINITE programming

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SIAM JOURNAL ON OPTIMIZATION 2009年第3期20卷 1311-1332页

作者： Fang, D. H. Li, C. Ng, K. F. Jishou Univ Coll Math & Comp Sci Jishou 416000 Peoples R China Zhejiang Univ Dept Math Hangzhou 310027 Peoples R China Chinese Univ Hong Kong Dept Math Hong Kong Hong Kong Peoples R China

For an inequality system defined by a possibly infinite family of proper functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions. Under the new constraint qualifications, we obtain characterizations of those reverse-convex inequalities which are a consequence of the constrained system, and we provide necessary and/or sufficient conditions for a stable Farkas lemma to hold. Similarly, we provide characterizations for constrained minimization problems to have the strong or strong stable Lagrangian dualities. Several known results in the conic programming problem are extended and improved.

关键词： convex inequality system Farkas lemma strong Lagrangian duality conic programming

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