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Matrix correction of a dual pair of improper linear programming problems

Computational Mathematics and Mathematical Physics 2007年第4期47卷 564-578页

作者： Erokhin, V.I. Borisoglebsk State Pedagogical University Borisoglebsk 397160 ul. Narodnaya 43 Russian Federation

A matrix is sought that solves a given dual pair of systems of linear algebraic equations. Necessary and sufficient conditions for the existence of solutions to this problem are obtained, and the form of the solutions is found. The form of the solution with the minimal Euclidean norm is indicated. Conditions for this solution to be a rank one matrix are examined. On the basis of these results, an analysis is performed for the following two problems: modifying the coefficient matrix for a dual pair of linear programs (which can be improper) to ensure the existence of given solutions for these programs, and modifying the coefficient matrix for a dual pair of improper linear programs to minimize its Euclidean norm. Necessary and sufficient conditions for the solvability of the first problem are given, and the form of its solutions is described. For the second problem, a method for the reduction to a nonlinear constrained minimization problem is indicated, necessary conditions for the existence of solutions are found, and the form of solutions is described. Numerical results are presented. © Nauka/Interperiodica 2007.

关键词： linear programming problems Methods for solving systems of linear algebraic equations Modifying the coefficient matrix

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Computationally Improved Optimal Deadlock Prevention Policy for linear programming problems of Flexible Manufacturing Systems

Computationally Improved Optimal Deadlock Prevention Policy ...

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IEEE International Conference on Systems, Man, and Cybernetics

作者： Yen-Liang Pan Mu-Der Jeng Sheng-Luen Chung Yu-Xin Guo Department of Avionic Engineering Air Force Academy Kaohsiung 820 Taiwan R.O.C. Department of Electrical Engineering National Taiwan Ocean University Department of Electrical Engineering National Taiwan University of Science and Technology

ISBN: (纸本)9781479906505

Deadlock prevention policies are used to solve the deadlock problems of flexible manufacturing systems. Theory of regions is the efficient method for obtaining optimal (i.e. maximally permissive) controllers. All legal and live maximal behavior can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, solving all sets of inequalities is very time-consuming. Moreover, the number of linear programming problems (LPPs) of all legal markings is also exponential with net size. In this paper, a novel methodology is proposed to reduce the number of MTSIs/ESSPs and LPPs. Preciously, one new concept called critical ones of crucial marking/transition-separation instances (COCMTSI) is developed and used in this deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks.

关键词： Petri nets linear programming problems deadlock prevention theory of regions flexible manufacturing system Flexible manufacturing systems Petri nets linear programming Policies Manufacturing systems

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Feasibility of piecewise-constant control sequences for timed continuous Petri nets

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AUTOMATICA 2013年第12期49卷 3654-3660页

作者： Leclercq, Edouard Lefebvre, Dimitri Univ Le Havre GREAH F-76600 Le Havre France

In this study, the determination of control actions for timed continuous Petri nets is investigated by the characterisation of attractive regions in marking space. In particular, attraction in finite time, which is important for practical issues, is considered. Based on the characterisation of attractive regions, the domain of admissible piecewise constant control actions is computed, and sufficient conditions to verify the feasibility of the control objectives are proposed. As a consequence, an iterative procedure is presented to compute piecewise constant control actions that correspond to local minimum time control for timed continuous Petri nets. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Petri nets Timed continuous Petri nets Control design linear programming problems

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Hybrid VNS-LP algorithm for online optimal coordination of directional overcurrent relays

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第23期14卷 5447-5455页

作者： Damchi, Yaser Dolatabadi, Mohammad Shahrood Univ Technol Fac Elect Engn & Robot Shahrood Iran Vali E Asr Univ Rafsanjan Dept Math Rafsanjan Iran

Optimal coordination of directional overcurrent relays (DOCRs) in interconnected power systems is a highly constrained, non-convex and non-linear optimisation problem. In this study, use of a series of linear programming (LP) problems in a variable neighbourhood search (VNS) framework is proposed, in which pickup current settings can be considered either as continuous or discrete variables. Therefore, the proposed hybrid algorithm (VNS-LP) is suitable for coordination problem-solving in a network with different types of DOCRs. Furthermore, two versions of the VNS algorithm are proposed, the first of which is very easy to implement, while, the other is somewhat more sophisticated, and at the same time much faster and possibly suitable for online coordination in smart grids applications. One advantage of the second algorithm is that it relies only on elementary arithmetic and requires low RAM, which makes it implementable in any low-level programming environment. This, in turn, can increase the interoperability, which is of crucial importance when automating tasks. The efficiency of the proposed algorithm was investigated in several test systems. Numerical results indicate that the two proposed approaches outperform the previous methods. Moreover, the coordination problem is solved in a reasonably short time using a faster approach.

关键词： smart power grids power system interconnection optimisation overcurrent protection relay protection search problems power system protection online optimal coordination directional overcurrent relays DOCR interconnected power systems nonconvex optimisation problem nonlinear optimisation problem linear programming problems variable neighbourhood search framework pickup current settings continuous variables discrete variables coordination problem-solving VNS algorithm online coordination smart grids applications low-level programming environment hybrid VNS-LP algorithm VNS framework elementary arithmetic RAM

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Positive filtering for positive 2D fuzzy systems under l1 performance

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IET CONTROL THEORY AND APPLICATIONS 2019年第7期13卷 1024-1030页

作者： Wang, Li Qun Chen, Xiaoming Shen, Jun Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Nanjing 210016 Jiangsu Peoples R China

In this study, the problem of positive filtering is investigated for positive two-dimensional (2D) Roesser T-S fuzzy systems under $\ell _{1}$l1-induced performance. Error-bounding positive filters are constructed to estimate the output of positive 2D T-S fuzzy systems. Firstly, a novel characterisation for asymptotic stability of the filtering error system with $\ell _{1}$l1-induced performance is derived. Then, based on that characterisation, sufficient conditions are derived to design the required filters expressed by linear programming problems. Finally, the theoretical results are illustrated through a numerical example.

关键词： fuzzy systems linear programming filtering theory asymptotic stability positive filtering positive 2D fuzzy systems two-dimensional Roesser T-S fuzzy systems error-bounding positive filters positive 2D T-S fuzzy systems filtering error system 1 performance linear programming problems asymptotic stability

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Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2019年第1期74卷 143-176页

作者： Cui, Yiran Morikuni, Keiichi Tsuchiya, Takashi Hayami, Ken UCL Dept Comp Sci Gower St London WC1E 6BT England Univ Tsukuba Div Informat Engn 1-1-1 Tennodai Tsukuba Ibaraki 3050006 Japan Natl Grad Inst Policy Studies Minato Ku 7-22-1 Roppongi Tokyo 1068677 Japan Natl Inst Informat Chiyoda Ku 2-1-2 Hitotsubashi Tokyo 1018430 Japan Grad Univ Adv Studies SOKENDAI Chiyoda Ku 2-1-2 Hitotsubashi Tokyo 1018430 Japan

We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe ill-conditioning of linear equations solved in the final phase of interior-point iterations. The Krylov subspace methods do not suffer from rank-deficiency and therefore no preprocessing is necessary even if rows of the constraint matrix are not linearly independent. By means of these methods, a new interior-point recurrence is proposed in order to omit one matrix-vector product at each step. Extensive numerical experiments are conducted over diverse instances of 140 LP problems including the Netlib, QAPLIB, Mittelmann and Atomizer Basis Pursuit collections. The largest problem has 434,580 unknowns. It turns out that our implementation is more robust than the standard public domain solvers SeDuMi (Self-Dual Minimization), SDPT3 (Semidefinite programming Toh-Todd-Tutuncu) and the LSMR iterative solver in PDCO (Primal-Dual Barrier Method for Convex Objectives) without increasing CPU time. The proposed interior-point method based on iterative solvers succeeds in solving a fairly large number of LP instances from benchmark libraries under the standard stopping criteria. The work also presents a fairly extensive benchmark test for several renowned solvers including direct and iterative solvers.

关键词： linear programming problems Interior-point methods Inner-iteration preconditioning Krylov subspace methods

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Generalized solution of linear systems and image restoration

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1999年第1期103卷 45-64页

作者： Aluffi-Pentini, F Castrignanò, T Maponi, P Parisi, V Zirilli, F Univ Rome La Sapienza Dipartimento Metodi & Modelli Matemat Rome Italy Univ Rome La Sapienza Dipartimento Matemat G Castelnuovo I-00185 Rome Italy Univ Roma Tor Vergata Dipartimento Fis Sez INFM I-00173 Rome Italy Univ Camerino Dipartimento Matemat & Fis I-62032 Camerino Italy

Let n, m be positive integers;we consider m x n real linear systems. We define regularized solutions of a linear system as the minimizers of an optimization problem. The objective function of this optimization problem can be seen as the Tikhonov functional when the p-norm is considered instead of the Euclidean norm. The cases p = 1 and p = infinity are studied. This analysis is used to restore defocused synthetic images and real images with encouraging results.

关键词： linear programming problems regularization procedures image restoration

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Estimating the size of the calling population in finite-source election queues by bilinear programming techniques

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MATHEMATICAL AND COMPUTER MODELLING 2007年第7-8期45卷 873-882页

作者： Belenky, A. S. NISTRAMAN Consulting Brookline MA 02446 USA MIT Ctr Engn Syst Fundamentals Cambridge MA 02139 USA

Finite source multi-server queuing systems represent a particular type of an exact model of voting places (precincts) servicing voters on the election day. The size of the calling population from which the arrivals (voters) come to vote in a precinct at each time segment of the election day is among key parameters of such systems. The problem of finding this parameter is formulated as the problem of maximizing the maximum function of a finite number of bilinear functions on polyhedra, and it can be solved with the use of bilinear programming techniques. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： bilinear programming problems finite source queuing systems linear programming problems precincts voter turnout voting machines

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Two Stage Indian Food Grain Supply Chain Network Transportation-Allocation Model

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IFAC-PapersOnLine 2016年第12期49卷 1767-1772页

作者： Mogale, D.G. Kumar, Sri Krishna Kumar Tiwari, Manoj Department of Industrial and Systems Engineering Indian Institute of Technology Kharagpur KharagpurWest Bengal721 302 India

This paper investigates the food grain supply chain, transportation allocation problem of Indian Public Distribution System (PDS). The different activities of Indian food grain supply chain are procurements, storage, movement, transportation and distribution. We have developed a mixed integer nonlinear programming model (MINLP) to minimize the transportation, inventory and operational cost of shipping food grains from the cluster of procurement centers of producing states to the consuming state warehouses. A recently developed chemical reaction optimization (CRO) algorithm is used for testing the model which gives the superior computational performance compared to other metaheuristics. © 2016

关键词： Food storage Chemical reactions Integer programming Nonlinear programming Supply chains Allocation problems Chemical reaction optimizations Computational performance Distribution systems Food grain Mixed integer non linear programming problems Mixed integer nonlinear programming models Supply chain network

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Finding Nonoscillatory Solutions to Difference Schemes for the Advection Equation

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第9期48卷 1646-1657页

作者： Kivva, S. L. Natl Acad Sci Ukraine Inst Math Machines & Syst UA-03187 Kiev Ukraine

The advection equation is solved using a weighted adaptive scheme that combines a monotone scheme with the central-difference approximation of the first spatial derivative. The determination of antidiffusion fluxes is treated as an optimization problem. The solvability of the optimization problem is analyzed, and the differential properties of the cost functional are examined. It is shown that the determination of antidiffusion fluxes is reduced to a linear programming problem in the case of an explicit scheme and to a nonlinear programming problem or a sequence of linear programming problems in the case of an implicit scheme. A simplified monotonization algorithm is proposed. Numerical results are presented.

关键词： advection equations difference schemes optimization problem linear programming problems

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