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State estimation via mathematical programming: a comparison of different estimation algorithms

IET GENERATION TRANSMISSION & DISTRIBUTION 2012年第6期6卷 545-553页

作者： Caro, E. Conejo, A. J. Tech Univ Madrid UPM Dept Stat Madrid Spain Univ Castilla La Mancha Dept Elect Engn E-13071 Ciudad Real Spain

Although the weighted least of squares technique is an efficient and well-established power system state-estimation procedure, a number of alternative estimation approaches have been proposed in the technical literature. This study presents and compares the most-common estimators formulating them as mathematical programming problems. The numerical accuracy and computational efficiency of the different estimators are analysed using an illustrative case study.

关键词： least squares approximations weighted least squares technique power system state-estimation procedure power system state estimation mathematical programming problems mathematical programming Interpolation and function approximation (numerical analysis) Power systems Optimisation techniques state estimation algorithm

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Nondominated equilibrium solutions of a multiobjective two-person nonzero-sum game and corresponding mathematical programming problem

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2007年第2期135卷 217-239页

作者： Nishizaki, I. Notsu, T. Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

With reference to a multiobjective two-person nonzero-sum game, we define nondominated equilibrium solutions and provide a necessary and sufficient condition for a pair of mixed strategies to be a nondominated equilibrium solution. Using the necessary and sufficient condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. We give a numerical example and demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical programming problem.

关键词： nondominated equilibrium solutions multiobjective two-person nonzero-sum games mathematical programming problems

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EQUILIBRIUM SOLUTIONS FOR MULTIOBJECTIVE BIMATRIX GAMES INCORPORATING FUZZY GOALS

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1995年第2期86卷 433-457页

作者： NISHIZAKI, I SAKAWA, M HIROSHIMA UNIV FAC ENGN DEPT IND & SYST ENGN HIGASHIHIROSHIMA 724 JAPAN

Equilibrium solutions in terms of the degree of attainment of a fuzzy goal for games in fuzzy and multiobjective environments are examined. We introduce a fuzzy goal for a payoff in order to incorporate ambiguity of human judgments and assume that a player tries to maximize his degree of attainment of the fuzzy goal. A fuzzy goal for a payoff and the equilibrium solution with respect to the degree of attainment of a fuzzy goal are defined. Two basic methods, one by weighting coefficients and the other by a minimum component, are employed to aggregate multiple fuzzy goals. When the membership functions are linear, computational methods for the equilibrium solutions are developed. It is shown that the equilibrium solutions are equal to the optimal solutions of mathematical programming problems in both cases. The relations between the equilibrium solutions for multiobjective bimatrix games incorporating fuzzy goals and the Pareto-optimal equilibrium solutions are considered.

关键词： BIMATRIX GAMES MULTIPLE PAYOFF MATRICES EQUILIBRIUM SOLUTIONS PARETO OPTIMALITY mathematical programming problems

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Traffic management system for smart road networks reserved for self-driving cars

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IET INTELLIGENT TRANSPORT SYSTEMS 2020年第9期14卷 1013-1024页

作者： Di Febbraro, Angela Gallo, Federico Giglio, Davide Sacco, Nicola Univ Genoa Dept Mech Energy Management & Transport Engn DIME Via Montallegro 1 I-16145 Genoa Italy Univ Genoa Italian Ctr Excellence Logist Transport & Infrast Via Vivaldi 5 I-16126 Genoa Italy

A model of a smart road network consisting of unsignalised intersections and smart roads connecting them is considered in this work with the aim of presenting a traffic management system for self-driving cars (or, more generally, autonomous vehicles) which travel the network. The proposed system repeatedly solves a set of mathematical programming problems (each of them relative to a single intersection or to a single road stretch of the network) within a decentralised control scheme in which each local intersection controller and each local road controller communicates with the fully autonomous vehicles in order to receive travel data from vehicles and to provide speed profiles to them once determined the optimal solution of the problem. In order to reduce the computational effort required to provide the optimal solution, a discrete-time approach is adopted so that, in each time interval, a limited number of vehicles are taken into consideration;in this way, solutions can be determined in a very short time thus making the proposed model compatible with a practical application to real traffic systems. The proposed model is general enough, and can be adapted to different scenarios of smart road networks reserved for self-driving cars.

关键词： mathematical programming decentralised control road traffic intelligent transportation systems mobile robots road vehicles discrete time systems fully autonomous vehicles optimal solution smart road network self-driving cars traffic management system single road stretch local intersection controller local road controller unsignalised intersections mathematical programming problems decentralised control discrete-time approach

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Geometric conditions for Kuhn-Tucker sufficiency of global optimality in mathematical programming

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2009年第2期194卷 363-367页

作者： Jeyakumar, V. Srisatkunarajah, S. Univ New S Wales Dept Appl Math Sydney NSW 2052 Australia

We present geometric criteria for a feasible point that satisfies the Kuhn-Tucker conditions to be it global minimizer of mathematical programming problems with or without bounds on the variables. The criteria apply to multi-extremal programming problems which may have several local minimizers that are not global. We establish such criteria in terms of underestimators of the Lagrangian of the problem. The underestimators are required to satisfy certain geometric property such as the convexity (or a generalized convexity) property. We show that the biconjugate of the Lagrangian can be chosen as a convex underestimator whenever the biconjugate coincides with the Lagrangian at a point. We also show how suitable underestimators can be constructed for the Lagrangian in the case where the problem has bounds on the variables. Examples are given to illustrate our results. (C) 2008 Published by Elsevier B.V.

关键词： mathematical programming problems Sufficient optimality conditions Multi-extremal problems Bounds on the variables Generalized convexity Underestimators

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Evaluate fuzzy Riemann integrals using the Monte Carlo method

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JOURNAL OF mathematical ANALYSIS AND APPLICATIONS 2001年第2期264卷 324-343页

作者： Wu, HC Natl Chi Nan Univ Dept Informat Management Puli 545 Nantou Taiwan

Techniques for using the Monte Carlo method to evaluate fuzzy Riemann integrals and improper fuzzy Riemann integrals are proposed in this paper. Owing to the alpha-level set of the (improper) fuzzy Riemann integral being the closed interval whose end points are the classical (improper) Riemann integrals, it is possible to invoke the Monte Carlo method to approximate the end points of the alpha-level closed intervals. We develop the strong law of large numbers for fuzzy random variables in order to give the techniques proposed for evaluating the (improper) fuzzy Riemann integrals using the Monte Carlo approach more theoretical support. The membership function of the (improper) fuzzy Riemann integral can be transformed into mathematical programming problems. Therefore, we can obtain the membership value by solving the mathematical programming problems using the commercial optimizer. (C) 2001 Elsevier Science.

关键词： fuzzy numbers (improper) fuzzy Riemann integrals Monte Carlo method strong law of large numbers mathematical programming problems

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Second-order necessary optimality conditions for a discrete optimal control problem with nonlinear state equations

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OPTIMAL CONTROL APPLICATIONS & METHODS 2020年第6期41卷 2250-2281页

作者： Toan, N. T. Thuy, L. Q. Ansari, Q. H. Yao, J-C Hanoi Univ Sci & Technol Sch Appl Math & Informat Hanoi Vietnam Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran Saudi Arabia China Med Univ Ctr Gen Educ Taichung Taiwan

In this article, we study second-order necessary optimality conditions for a discrete optimal control problem with a nonconvex cost function, nonlinear state equations and mixed constraints. In order to achieve these conditions, we first establish an abstract result on the second-order necessary optimality conditions for a mathematical programming problem and then we derive the second-order necessary optimality conditions for a discrete optimal control problem. The main result of this article is illustrated by two examples.

关键词： discrete optimal control problems first-order optimality condition mathematical programming problems nonlinear state equation second-order optimality condition

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Solving the Disclosure Auditing Problem for Secondary Cell Suppression by Means of Linear programming

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TRANSACTIONS ON DATA PRIVACY 2020年第2期13卷 67-90页

作者： de Waal, Ton Coutinho, Wieger Stat Netherlands POB 24500 NL-2490 HA The Hague Netherlands Tilburg Univ POB 90153 NL-5000 LE Tilburg Netherlands Dunea Pl Verenigde Naties 11-15 NL-2719 EG Zoetermeer Netherlands

National Statistical Institutes (NSIs) have the obligation to protect the privacy of individual persons or enterprises against disclosure of potentially sensitive information. For this reason, NSIs protect tabular data against disclosure of sensitive information before they are released. For tabular magnitude data, the starting point of this protection process usually is a sensitivity measure for individual cells. Such a sensitivity measure defines when a cell value is considered safe for publication or not. An often used method to protect a table with unsafe cells against disclosure of sensitive information is cell suppression. [5] argues that the standard criterion for deciding whether a table after suppression is safe or not is somewhat inconsistent and proposes a new criterion. [5] also gives a mixed-integer programming problem formulation for applying this new criterion. The problem with that formulation is that it is quite large and very hard to solve for even moderately sized tables. To be more precise, that mixed-integer programming problem formulation suggests that the auditing problem based on the criterion of [5] is NP-hard. The general assumption among operations research experts is that the computing time for NP-hard problems is non-polynomial in their input parameters. In the current paper, we propose solving a number of smaller and computationally much easier linear programming problems instead of solving one large mixed-integer programming problem. Solving linear programming problems can be done in time polynomial in their input parameters.

关键词： Cell Suppression mathematical programming problems Sensitivity measures Statistical disclosure control Tabular magnitude data

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