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12th International Conference on Fuzzy Systems and Knowledge Discovery (FSKD)

作者： Li, Yanfang Duan, Xibo Gu, Jia Shandong Coll Electon Technol Dept Basic Educ Jinan 250200 Peoples R China Shandong Water Polytech Dept Basic Sci Rizhao 276826 Peoples R China Shanghai Univ Engn Sci Coll Fundamental Studies Shanghai 201620 Peoples R China

ISBN: (纸本)9781467376822

In this article, we extend kernel-based interior point algorithms for linear programming to convex quadratic programming overs second-order cones. By means of Jordan algebras, we establish the iteration complexity for long-and short-step interior-point methods, namely, O (3 root N-2 log N/epsilon) and O (root N log N/epsilon), respectively. These results coincide with the ones obtained in the linear programming case.

关键词： Convex quadratic programming interior point algorithms Long- and short-step methods Jordan algebras iteration complexity

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ON THE FINITE CONVERGENCE OF interior-point algorithms FOR LINEAR-PROGRAMMING

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MATHEMATICAL PROGRAMMING 1992年第2期57卷 325-335页

作者： YE, YY 1. Department of Management Sciences The University of Iowa 52242 Iowa City IA USA

It has been shown [8] that numerous interior-point algorithms for linear programming (LP) generate solution sequences that converge to strict complementarity solutions, or interior solutions on the optimal face. In this note we further establish a theoretical base for Gay's test (Gay, 1989) to identify the optimal face, and develop a new termination procedure to obtain an exact solution on the optimal face. We also report some numerical results for solving a set of LP test problems, each of which has a highly degenerate and unbounded optimal face.

关键词： STRICT COMPLEMENTARITY interior point algorithms LINEAR PROGRAMMING OPTIMAL FACE

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CONVERGENCE BEHAVIOR OF interior-point algorithms

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MATHEMATICAL PROGRAMMING 1993年第2期60卷 215-228页

作者： GULER, O YE, YY UNIV IOWA DEPT MANAGEMENT SCIIOWA CITYIA 52242

We show that most interior-point algorithms for linear programming generate a solution sequence in which every limit point satisfies the strict complementarity condition. These algorithms include all path-following algorithms and some potential reduction algorithms. The result also holds for the monotone complementarity problem if a strict complementarity solution exists. In general, the limit point is a solution that maximizes the number of its nonzero components among all solutions.

关键词： STRICT COMPLEMENTARITY MAXIMAL COMPLEMENTARITY interior point algorithms LINEAR PROGRAMMING MONOTONE COMPLEMENTARITY PROBLEM

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ON ADAPTIVE-STEP PRIMAL-DUAL interior-point algorithms FOR LINEAR-PROGRAMMING

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MATHEMATICS OF OPERATIONS RESEARCH 1993年第4期18卷 964-981页

作者： MIZUNO, S TODD, MJ YE, YY CORNELL UNIV SCH OPERAT RES & IND ENGNITHACANY 14853 UNIV IOWA DEPT MANAGEMENT SCIIOWA CITYIA 52242

We describe several adaptive-step primal-dual interior point algorithms for linear programming. All have polynomial time complexity while some allow very long steps in favorable circumstances. We provide heuristic reasoning for expecting that the algorithms will perform much better in practice than guaranteed by the worst-case estimates, based on an analysis using a nonrigorous probabilistic assumption.

关键词： LINEAR PROGRAMMING interior point algorithms PATH-FOLLOWING algorithms POTENTIAL REDUCTION algorithms

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Proximity queries between convex objects: An interior point approach for implicit surfaces

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IEEE TRANSACTIONS ON ROBOTICS 2008年第1期24卷 211-220页

作者： Chakraborty, Nilanjan Peng, Jufeng Akella, Srinivas Mitchell, John E. Rensselaer Polytech Inst Dept Comp Sci Troy NY 12180 USA Rensselaer Polytech Inst Dept Math Sci Troy NY 12180 USA

This paper presents a general method for exact distance computation between convex objects represented as intersections of implicit surfaces. Exact distance computation algorithms are particularly important for applications involving objects that make intermittent contact, such as in dynamic simulations and in haptic interactions. They can also be used in the narrow phase of hierarchical collision detection. In contrast to geometric approaches developed for polyhedral objects, we formulate the distance computation problem as a convex optimization problem. We use an interior point method to solve the optimization problem and demonstrate that, for general convex objects represented as implicit surfaces, interior point approaches are globally convergent, and fast in practice. Further, they provide polynomial-time guarantees for implicit surface objects when the implicit surfaces have self-concordant barrier functions. We use a primal-dual interior point algorithm that solves the Karush-Kuhn-Tucker (KKT) conditions obtained from the convex programming formulation. For the case of polyhedra and quadrics, we establish a theoretical time complexity of O(n(1.5)), where n is the number of constraints. We present implementation results for example implicit surface objects, including polyhedra, quadrics, and generalizations of quadrics such as superquadrics and hyperquadrics, as well as intersections of these surfaces. We demonstrate that in practice, the algorithm takes time linear in the number of constraints, and that distance computation rates of about 1 kHz can be achieved. We also extend the approach to proximity queries between deforming convex objects. Finally, we show that continuous collision detection for linearly translating objects can be performed by solving two related convex optimization problems. For polyhedra and quadrics, we establish that the computational complexity of this problem is also O(n(1.5)).

关键词： closest points collision detection implicit surfaces interior point algorithms proximity query

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A new long-step interior point algorithm for linear programming based on the algebraic equivalent transformation

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CENTRAL EUROPEAN JOURNAL OF OPERATIONS RESEARCH 2023年第3期31卷 691-711页

作者： E-Nagy, Marianna Varga, Anita Budapest Univ Technol & Econ Inst Math Dept Differential Equat Muegyet Rkp 3 H-1111 Budapest Hungary Corvinus Univ Budapest Corvinus Ctr Operat Res Fovam Ter 8 H-1093 Budapest Hungary

In this paper, we investigate a new primal-dual long-step interior point algorithm for linear optimization. Based on the step size, interior point algorithms can be divided into two main groups, short-step, and long-step methods. In practice, long-step variants perform better, but usually, a better theoretical complexity can be achieved for the short-step methods. One of the exceptions is the large-update algorithm of Ai and Zhang. The new wide neighborhood and the main characteristics of the presented algorithm are based on their approach. In addition, we use the algebraic equivalent transformation technique of Darvay to determine new modified search directions for our method. We show that the new long-step algorithm is convergent and has the best known iteration complexity of short-step variants. We present our numerical results and compare the performance of our algorithm with two previously introduced Ai-Zhang type interior point algorithms on a set of linear programming test problems from the Netlib library.

关键词： Mathematical programming Linear optimization interior point algorithms Algebraic equivalent transformation technique

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RECOVERING AN OPTIMAL LP BASIS FROM AN interior-point SOLUTION

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OPERATIONS RESEARCH LETTERS 1994年第4期15卷 169-178页

作者： BIXBY, RE SALTZMAN, MJ CLEMSON UNIV CLEMSONSC 29631 RICE UNIV DEPT COMPUTAT & APPL MATHHOUSTONTX 77251

An important issue in the implementation of interior point algorithms for linear programming is the recovery of an optimal basic solution from an optimal interior point solution. In this paper we describe a method for recovering such a solution. Our implementation links a high-performance interior point code (OBI) with a high-performance simplex code (CPLEX). Results of our computational tests indicate that basis recovery can be done quickly and efficiently.

关键词： PROGRAMMING (LINEAR PROGRAMMING interior point algorithms SIMPLEX METHOD BASIS RECOVERY) ANALYSIS OF algorithms (DATA STRUCTURES algorithms FOR BASIS RECOVERY)

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Presolve analysis and interior point solutions of the linear programming coordination problem of directional overcurrent relays

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2001年第8期23卷 819-825页

作者： Urdaneta, AJ Pérez, LG Gómez, JF Feijoo, B González, M Univ Simon Bolivar Dept Convers & Transporte Energia Caracas 1080 Venezuela

A linear programming interior point algorithm is proposed for the solution of the problem of coordinating directional overcurrent relays in interconnected power systems considering definite time backup relaying. The proposed algorithm is a variation of the primal-dual approach that uses multiple correctors of centrality. Pre-solution problem filtering simplification techniques are used prior to the application of the linear programming algorithm. Results are presented for the application of the methodology on a realistic test case, a 115-69 kV power system with 108 buses, 86 lines, 61 transformers, and 97 directional overcurrent relays. Optimal solutions are found in an automatic fashion, using the algorithm for the settings of the ground relays as well as for the phase relays. The application of the pre-solution problem simplification techniques is highly recommended, resulting in a significant reduction of the size and complexity of the linear programming problem to be solved. The interior point approach reaches a feasible point in the close vicinity of the final optimal result in only one or two iterations. This fact represents an advantage for on-line applications. The proposed methodology and in particular the use of the presolve problem simplification techniques is shown as a new valuable tool for the setting of directional overcurrent relays in interconnected power systems. (C) 2001 Elsevier Science Ltd. All rights reserved.

关键词： power system protection relay coordination linear programming interior point algorithms

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Non-negatively constrained image deblurring with an inexact interior point method

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2009年第1期231卷 236-248页

作者： Bonettini, Silvia Serafini, Thomas Univ Ferrara Dipartimento Matemat I-44100 Ferrara Italy Univ Modena & Reggio Emilia Dipartimento Matemat Modena Italy

Nonlinear image deblurring procedures based on probabilistic considerations have been widely investigated in the literature. This approach leads to model the deblurring problem as a large scale optimization problem, with a nonlinear, convex objective function and non-negativity constraints on the sign of the variables. The interior point methods have shown in the last years to be very reliable in nonlinear programs. In this paper we propose an inexact Newton interior point (IP) algorithm designed for the solution of the deblurring problem. The numerical experience compares the IP method with another state-of-the-art method, the Lucy Richardson algorithm, and shows a significant improvement of the processing time. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Image deblurring Deconvolution methods interior point algorithms Regularization techniques

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An interior point method for solving systems of linear equations and inequalities

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OPERATIONS RESEARCH LETTERS 2000年第3期27卷 101-107页

作者： Kallio, M Salo, S Helsinki Sch Econ Helsinki 00100 Finland

A simple interior point method is proposed for solving a system of linear equations subject to nonnegativity constraints. The direction of update is defined by projection of the current solution on a linear manifold defined by the equations. Infeasibility is discussed and extension for free and bounded variables is presented. As an application, we consider linear programming problems and a comparison with a state-of-the-art primal-dual infeasible interior point code is presented. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： interior point algorithms linear inequalities linear programming

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