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Lower bound limit and shakedown analysis of orthotropic material

MATHEMATICS AND MECHANICS OF SOLIDS 2020年第11期25卷 2037-2049页

作者： Qin, Fang Zhang, Lele Chen, Geng Broeckmann, Christoph Beijing Jiaotong Univ Sch Mech Elect & Control Engn Shangyuancun 3 Beijing Peoples R China IAV GmbH Gifhorn Germany Rhein Westfal TH Aachen Inst Mat Applicat Mech Engn Aachen Germany

We present in this study a new approach for predicting the plastic and shakedown limits of structures composed of orthotropic materials. In this approach, the Hill yield criterion is introduced to Melan's theorem. By formulating the problem by means of the finite element method and solving the resulting large-scale nonlinear optimization problem we successfully predict the plastic and shakedown limits of structures having complex geometries made from multi-orthotropic materials. Several numerical examples are elaborated in this study for evaluating the accuracy, general applicability, as well as the efficiency of the established numerical scheme. Overall, the study confirms that the direct method can be extended and adopted as a viable means for design and analysis of structures made of orthotropic materials.

关键词： Shakedown analysis lower bound analysis orthotropic material Hill yield criterion large-scale nonlinear programming IPOPT

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Optimizing Control for large scale Dynamic Systems;General Issues and Case Study Results: Transmission Operations Optimizer for Toronto Water System 23

Optimizing Control for Large Scale Dynamic Systems;General I...

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23rd International Conference on Engineering, Technology and Innovation (ICE/ITMC)

作者： Malinowski, Krzysztof Blaszczyk, Jacek Allidina, Alnoor Warsaw Univ Technol Inst Control & Computat Engn Warsaw Poland Res & Acad Comp Network Inst NASK Warsaw Poland IBI Grp Toronto ON Canada

ISBN: (纸本)9781538607749

The aim of this paper is to provide a concise yet still a broad view on the most important differences between both objectives and design of regulatory control on one side and optimizing control of large supply and/or distribution systems. For this purpose the main objectives and characteristics of both types of control are first briefly presented. The main differences are exposed and discussed, followed by the description of problems related to introducing and, eventually, to implementing optimizing control systems. The second part of the paper is devoted to short presentation of a major optimizing controller for very large municipal water supply system, namely Toronto Water System (TWS). The Transmission Operations Optimizer (TOO) has been recently being tested and gradually implemented at Toronto Water Control Center and found to provide for meaningful electrical energy savings and much improved system operations.

关键词： optimizing control large scale dynamic systems large-scale nonlinear programming minimum cost operative planning optimal pump scheduling water supply hydraulic simulations

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Simulation-based Optimization Methods Applied to large scale Water Systems Control 13

Simulation-based Optimization Methods Applied to Large Scale...

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Conference on UIC/ATC/ScalCom/CBDCom/IoP/SmartWorld

作者： Niewiadomska-Szynkiewicz, Ewa Blaszczyk, Jacek NASK Res & Acad Comp Network Ul Wawozowa 18 PL-02796 Warsaw Poland Warsaw Univ Technol Inst Control & Computat Engn Ul Nowowiejska 15-19 PL-00665 Warsaw Poland

ISBN: (纸本)9781509027712

Recent progress in computer science put forwards the research and applications of simulation-based optimization methods in applied science and engineering. This paper is concerned with computational research for complex environmental systems. The simulation-based optimization approach and numerical techniques that optimize performance of system by using simulation to evaluate the objective value are reviewed and discussed. The attention is focused on the application of this approach to operational management of large scale water systems. The results of two case studies are presented and discussed - flood control in the multireservoir water system in Poland and optimal control of the water distribution system in Canada.

关键词： Simulation-based optimization Flood management Multireservoir systems large-scale nonlinear programming Minimum cost operative planning Optimal pump scheduling Water supply Hydraulic simulations

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Aggregated Pumping Station Operation Planning Problem (APSOP) for large scale Water Transmission System

Aggregated Pumping Station Operation Planning Problem (APSOP...

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10th Nordic International Conference on Applied Parallel Computing - State of the Art in Scientific and Parallel Computing (PARA)

作者： Blaszczyk, Jacek Malinowski, Krzysztof Allidina, Alnoor Res & Acad Comp Network NASK Ul Wawozowa 18 PL-02796 Warsaw Poland Warsaw Univ Technol Fac Elect & Informat Technol Inst Control & Computat Engn PL-00665 Warsaw Poland IBI MAAK Inc Richmond Hill ON L4B 4N1 Canada

ISBN: (纸本)9783642281501;9783642281518

large scale potable water transmission system considered in this paper is the Toronto Water System (TWS), one of the largest existing potable water supply networks. The main objective of the ongoing Transmission Operations Optimizer (TOO) project consists of developing an advanced tool for providing pumping schedules for 153 TWS pumps, with all quantitative requirements with respect to system operation being met while the energy costs are minimized ("The aim of pump scheduling is to minimize the marginal cost of supplying water while keeping within physical and operational constraints, such as maintaining sufficient water within the system's reservoirs, to meet the required time-varying consumer demands." - [6]). It is assumed that TOO should produce detailed optimal schedules for all pumps. The following modules of TOO are being currently developed: demand forecasting module, energy rates forecasting module, pumping schedule optimizer and, finally, an assessment module consisting mainly of hydraulic, EPANET based, TWS simulator. This paper presents key component of the pumping schedule optimizer, namely, the Aggregated Pumping Station Operation Planning Problem (APSOP) and the approach to its solution.

关键词： water supply minimum cost operation planning large-scale nonlinear programming

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Iterative solution of augmented systems arising in interior methods

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SIAM JOURNAL ON OPTIMIZATION 2007年第2期18卷 666-690页

作者： Forsgren, Anders Gill, Philip E. Griffin, Joshua D. Royal Inst Technol Dept Math SE-10044 Stockholm Sweden Univ Calif San Diego Dept Math La Jolla CA 92093 USA Sandia Natl Labs Livermore CA 94551 USA

Iterative methods are proposed for certain augmented systems of linear equations that arise in interior methods for general nonlinear optimization. Interior methods de. ne a sequence of KKT equations that represent the symmetrized ( but indefinite) equations associated with Newton's method for a point satisfying the perturbed optimality conditions. These equations involve both the primal and dual variables and become increasingly ill- conditioned as the optimization proceeds. In this context, an iterative linear solver must not only handle the ill- conditioning but also detect the occurrence of KKT matrices with the wrong matrix inertia. A one- parameter family of equivalent linear equations is formulated that includes the KKT system as a special case. The discussion focuses on a particular system from this family, known as the " doubly augmented system," that is positive definite with respect to both the primal and dual variables. This property means that a standard preconditioned conjugate- gradient method involving both primal and dual variables will either terminate successfully or detect if the KKT matrix has the wrong inertia. Constraint preconditioning is a well- known technique for preconditioning the conjugate- gradient method on augmented systems. A family of constraint preconditioners is proposed that provably eliminates the inherent ill- conditioning in the augmented system. A considerable benefit of combining constraint preconditioning with the doubly augmented system is that the preconditioner need not be applied exactly. Two particular " active- set" constraint preconditioners are formulated that involve only a subset of the rows of the augmented system and thereby may be applied with considerably less work. Finally, some numerical experiments illustrate the numerical performance of the proposed preconditioners and highlight some theoretical properties of the preconditioned matrices.

关键词： large-scale nonlinear programming nonconvex optimization interior methods augmented systems KKT systems iterative methods conjugate-gradient method constraint preconditioning

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Mean value cross decomposition for nonlinear convex problems

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OPTIMIZATION METHODS & SOFTWARE 2006年第3期21卷 401-417页

作者： Holmberg, K Kiwiel, KC Linkoping Univ Linkoping Inst Technol SE-58183 Linkoping Sweden Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland

Mean value cross decomposition is a symmetric primal-dual decomposition method suitable for optimization problems with both primal and dual structures. It uses only easily solvable subproblems and no difficult master problems. Originally developed for linear problems, it is in this paper extended to nonlinear convex optimization problems. Convergence is proved for a somewhat generalized version, allowing more general weights. Computational results are presented for a network routing problem with congestion costs, a large-scale nonlinear problem with structures that enable decomposition both with respect to variables and constraints. The main goals of the tests are to illustrate the procedure and to indicate that this decomposition approach is more efficient than direct solution with a well established general code.

关键词： mathematical programming large-scale nonlinear programming decomposition methods

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Truncated dual SQP method with limited memory

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OPTIMIZATION METHODS & SOFTWARE 1995年第1期6卷 25-57页

作者： Ni, Q NANJING UNIV DEPT MATHNANJING 210008PEOPLES R CHINA

This paper represents a truncated dual sequential quadratic programming method with limited memory, which can solve sparse and dense large-scale nonlinear programming problems. Because an approximation of the inverse Hessian matrix of the Lagrangian function is formulated in a dual quadratic programming subproblem with simple bounds, the computation of the inverse matrix in the subproblem is avoided. A truncated solution of the dual quadratic programming subproblem is determined by an iterative method, in which the computation of the matrix-vector product, instead of the matrix factorization, is needed such that the implementation at each iteration is relatively simple and time-economic. With the technique of a limited memory update, the estimated inverse Hessian matrix of the Lagrangian function is computed and stored by means of some vectors, and this decreases the computation in solving the dual quadratic programming subproblem. The global convergence of the algorithm is proved and the numerical results on small and large test problems are given.

关键词： limited memory SQP method large-scale nonlinear programming

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A Generalized Reduced Gradient Algorithm for Solving large-scale Discrete-Time nonlinear Optimal Control Problems

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IFAC Proceedings Volumes 1989年第2期22卷 45-50页

作者： J.L.D. Facó INRIA Rocquencourt 78153 Le Chesnay France

nonlinear dynamical control systems are considered in a unified approach as discrete-time nonlinear optimal control problems with time delays and inequality constraints on the state and the control variables (usually double bounds). These problems are in general large-scale and efficient numerical solutions can be obtained by constrained nonlinear programming methods if reliable techniques able to deal with these numerical difficulties are employed. A generalized reduced gradient algorithm is proposed exploiting the staircase structure of the jacobian matrix of the dynamic equations by using some priority principles on the partition of the variables into basic and independent sets for each time period when a reenversion is needed, and for choosing a substitute basic variable when change-of-basis occur for regularity reasons. Factorized representations of the basic matrix facilitate the resolutions of the linear systems of equations in different parts of the algorithm. Gaussian eliminations (LU decompositions) of the diagonal blocks of the main factor of the representation improve the numerical stability of these processes. In the reduced dimension space of the bounded independent variables we have an unconstrained differentiable nonlinear objective function. The search directions can be computed by adapted unconstrained optimization methods with memory limitation as Conjugate Gradients. If some amount of extra storage is available, limited-storage methods combining properties of the quasi- Newton BFGS and conjugate gradients methods present superior convergence rates. These alternative search directions can improve the convergence of the algorithm. Time delays in the nonlinear dynamic equations can be considered by some specific sparse matrix techniques with no influence on the algorithm main strategy. A computer code has been designed and numerical experiments with different optimization models for applications to electric power generation planning, macroeconomy an

关键词： nonlinear control systems large-scale nonlinear programming reduced gradient method limited-storage quasi-Newton algorithms

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Computational advances in large-scale nonlinear optimization

Computational advances in large-scale nonlinear optimization

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作者： Dean, Dennis Ross Naval Postgraduate School

学位级别：硕士

This is a comparison of two state-of-the-art large-scale nonlinear optimization systems exhibiting unprecedented problem solution capabilities both in size of problem handled and method of solution. These codes are MINOS, developed by B. A. Murtagh and M. A. Saunders, and XS, developed by G. G. Brown and G. W. Graves. The codes are evaluated with respect to their problem solving capabilities and potential for practical applica- tion by analysts. Computational results are presented for thirteen nonlinear and nonlinear mixed integer test problems with from two to 793 variables (12 to 100 integer variables) and one to 401 constraints. Portions of this work were presented at the CORS/ORSA/TIMS joint meeting in Toronto, May 1981.

关键词： large-scale nonlinear programming optimization large-scale linear programming mixed integer programming algorithm evaluation nonlinear test problems

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