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STOCHASTIC AND ROBUST-CONTROL OF NONLINEAR ECONOMIC-SYSTEMS

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1994年第2期73卷 304-318页

作者： RUSTEM, B UNIV LONDON IMPERIAL COLL SCI TECHNOL & MED DEPT COMP 180 QUEENS GATE LONDON SW7 2BZ ENGLAND

In this paper, we use a robust policy concept that is an extension to nonlinear systems of the mean-variance approach for linear models. In the linear case, the approach reduces to the minimization of a convex combination of the mean and variance of the stochastic problem. We also discuss a method for computing expectations of nonlinear systems based on evaluating the bias from certainty equivalence using Monte Carlo simulations. The method computes robust strategies. If desired, these can be in the form of simple decision rules, as aggregate parametrisations of full feedback strategies. The parameters are determined to minimize a convex combination of the original objective function and a sensitivity (variance) expression. The latter can either be chosen as the sensitivity (variance) of the original objective function or the sensitivity (variance) of the individual endogenous variables.

关键词： NONLINEAR programming STOCHASTIC PROCESSES ECONOMICS OPTIMIZATION CONTROL parametric programming

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An O(n²) active set algorithm for solving two related box constrained parametric quadratic programs

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NUMERICAL ALGORITHMS 2001年第4期27卷 367-375页

作者： Gómez, MA Univ A Coruna Sch Econ La Coruna 15071 Spain

Recently, O(n(2)) active set methods have been presented for minimizing the parametric quadratic functions (1/2)x' Dx - a'x + lambda/gamma'x - c\ and (1/2)x' Dx - a'x + (lambda/2)(gamma'x - c)(2), respectively, subject to l less than or equal to x less than or equal to b, for all nonnegative values of the parameter lambda. Here, D is a positive diagonal n x n matrix, gamma and a are arbitrary n-vectors, c is an arbitrary scalar;l and b are arbitrary n-vectors such that l less than or equal to b. In this paper, we show that each one of these algorithms may be used to simultaneously solve both parametric programs with no additional computational cost.

关键词： nonlinear programming quadratic programming parametric programming

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Fault-Tolerant Control of an Hexarotor Unmanned Aerial Vehicle Applying Outdoor Tests and Experiments

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IFAC-PapersOnLine 2018年第22期51卷 312-317页

作者： Mazeh, Hussein Saied, Majd Shraim, Hassan Francis, Clovis Lebanon

This paper presents a fault-tolerant control approach for actuators failures in multirotor Unmanned Aerial Vehicles UAVs. The strategy is applied on an hexarotor UAV. First, the hexarotor model is derived by means of the Newton-Euler formalism. A Controllability study based on the modified Kalman Rank condition is presented in case of one or more failing motors. A control allocation based recovery strategy is applied on the hexarotor when it is controllable. The control allocation problem is stated using a parametric programming formulation and is solved for an explicit solution. Outdoor real-time experimental results demonstrate the effectiveness of the applied strategy. © 2018

关键词： Aircraft control Actuators Antennas Fault tolerance Unmanned aerial vehicles (UAV) Control allocation Control allocation problem Controllability studies Explicit solutions Fault tolerant control Hexarotor parametric programming Recovery strategies

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AN ALGORITHM FOR FRACTIONAL ASSIGNMENT PROBLEMS

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DISCRETE APPLIED MATHEMATICS 1995年第2-3期56卷 333-343页

作者： SHIGENO, M SARUWATARI, Y MATSUI, T SCI UNIV TOKYO DEPT MANAGEMENT SCISHINJUKU KUTOKYO 162JAPAN NATL DEF ACAD DEPT SOCIAL SCIYOKOSUKAKANAGAWA 239JAPAN UNIV TOKYO FAC ENGNDEPT MATH ENGN & INFORMAT PHYSBUNKYO KUTOKYO 113JAPAN

In this paper, we propose a polynomial-time algorithm for fractional assignment problems. The fractional assignment problem is interpreted as follows. Let G=(I,J,E) be a bipartite graph where I and J are vertex sets and E subset of or equal to I x J is an edge set. We call an edge subset X( subset of or equal to E) an assignment if every vertex is incident to exactly one edge from X. Given an integer weight c(ij) and a positive integer weight d(ij) for every edge (i,j) is an element of E, the fractional assignment problem finds an assignment X( subset of or equal to E) such that the ratio (Sigma(i,j) is an element of X) C-ij)/(Sigma((i,j) is an element of X d(ij)) is minimized. Some algorithms were developed for the fractional assignment problem. Recently, Radzik (1992) showed that an algorithm which is based on the parametric approach and Newton's method is the fastest one among them. Actually, it solves the fractional assignment problem in O(root nm log(2)(nCD)/(1 + log log(nCD)- log log(nD))) time where \I\ = \J\ = n, \E\ = m, C = max {1, max {\c(ij)\ :(i,j) is an element of E}} and D = max {d(ij):(i,j) is an element of E} + 1. Our algorithm developed in this paper is also based on the parametric approach, but it is combined with the approximate binary search method. The time complexity of our algorithm is O(root nm log D log(nCD)) time, and provides with a better time bound than the above algorithm.

关键词： COMBINATORIAL OPTIMIZATION MATHEMATICAL programming FRACTIONAL programming ASSIGNMENT PROBLEMS APPROXIMATION OPTIMALITY parametric programming

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Modeling diminishing marginal returns in a hierarchical inventory system of reparable spare parts

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ANNALS OF OPERATIONS RESEARCH 1999年第91期91卷 319-337页

作者： Zorn, WL Deckro, RF Lehmkuhl, LJ USAF Dept Operat Sci Inst Technol Wright Patterson AFB OH 45433 USA USAF Acad Dept Math Sci Colorado Springs CO 80840 USA

Safety stock levels of reparable spare parts in a hierarchical inventory structure are determined relative to the marginal improvement to end item availability provided by each stock level. This research is focused on the United States Air Force (USAF) hierarchical inventory and repair system as modeled by the Multi-Echelon-Technique-for-Recoverable-Item-Control (METRIC) methodology. A piecewise linear modeling framework is introduced based on output from the Aircraft Availability Model (AAM), a model that is part of the METRIC family of models. The underlying nature of the piecewise linear formulation provides integer stock levels with continuous decision variables. This model provides the highest attainable end-item availability relative to an inventory of reparable spare parts. Additionally, the model provides a robust platform for the conduct of extensive post-optimality analysis. While this research focuses on the METRIC family of models, the methodology developed may be applied to any hierarchical inventory of reparable spares that conforms to the model's underlying mathematical structure.

关键词： hierarchical inventory systems linear programming parametric programming reparable spares

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Two bi-objective optimization models for competitive location problems

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INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING 2006年第3期5卷 531-543页

作者： Yang, Fengmei Hua, Guowei Inoue, Hiroshi Shi, Jianming Muroran Inst Technol Dept Comp Sci & Syst Engn Muroran Hokkaido 0508585 Japan Tokyo Univ Sci Sch Management Kuki Saitama 3468512 Japan Beijing Univ Chem Technol Fac Sci Beijing 100029 Peoples R China

This paper deals with two bi-objective models arising from competitive location problems. The first model simultaneously intends to maximize market share and to minimize cost. The second one aims to maximize both profit and the profit margin. We study some of the related properties of the models, examine relations between the models and a single objective parametric integer programming problem, and then show how both bi-objective location problems can be solved through the use of a single objective parametric integer program. Based on this, we propose two methods of obtaining a set of efficient solutions to the problems of fundamental approach. Finally, a numerical example is presented to illustrate the solution techniques.

关键词： facilities competitive location bi-objective parametric programming

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Ibm :: Generalinfo :: E20-8171 an Introduction to Linear programming 1964

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2016年

[Auto Generated] Chapter 1: Concepts and Examples . 1 Distillate (heating oil) Blending. 26 Fuel Blending . 27 1.1: Example of Production Capacity 3.3: The Objective Function Allocation . 2 and Constraints 27 1. 2: Example of Feed Blending 7 Objective Function . 27 1. 3: Example of Investment Policy 9 Material-Balance Constraints 27 1. 4: Characteristics of a Linear Pipe-Still Constraints. 27 programming Application. 13 Cat-Cracker Constraint 27 1. 5: Typical Linear programming Fuel Oil-Blending

关键词： deluxe models e20-8171 feasible feasible solution generalinfo hex nuts introduction linear linear programming marginal values matrix objective objective function optimum optimum policy parametric programming profit programming simplex method solution variable variables virgin naphtha

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Time-cost trade-off analysis of project networks in fuzzy environments

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第2期212卷 386-397页

作者： Chen, Shih-Pin Tsai, Ming-Jiun Natl Chung Cheng Univ Dept Business Adm Chiayi 621 Taiwan

This paper proposes a novel approach for time-cost trade-off analysis of a project network in fuzzy environments. Different from the results of previous studies, in this paper the membership function of the fuzzy minimum total crash cost is constructed based on Zadeh's extension principle and fuzzy solutions are provided. A pair of two-level mathematical programs parameterized by possibility level alpha is formulated to calculate the lower and upper bounds of the fuzzy minimum total crash cost at alpha. By enumerating different values of alpha, the membership function of the fuzzy minimum total crash cost is constructed, and the corresponding optimal activity time for each activity is also obtained at the same time. An example of time-cost trade-off problem with several fuzzy parameters is solved successfully to demonstrate the validity of the proposed approach. Since the minimum total crash cost is expressed by a membership function rather than by a crisp value, the fuzziness of parameters is conserved completely, and more information is provided for time-cost trade-off analysis in project management. The proposed approach also can be applied to time-cost trade-off problems with other characteristics. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Fuzzy sets Project management Time-cost trade-off Crash parametric programming

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parametric optimization with uncertainty on the left hand side of linear programs

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COMPUTERS & CHEMICAL ENGINEERING 2014年 60卷 31-40页

作者： Khalilpour, Rajab Karimi, I. A. Natl Univ Singapore Dept Chem & Biomol Engn Singapore 117576 Singapore

Although parametric optimization with uncertainties on the objective function (OF) or on the so-called "right-hand-side" (RHS) of the constraints has been addressed successfully in recent papers, very little work exists on the same with uncertainties on the left-hand-side (LHS) of the constraints or in the coefficients of the constraint matrix. The goal of this work has been to develop a systematic method to solve such parametric optimization problems. This is a very complex problem and we have begun with the simplest of optimization problems, namely the linear programming problem with a single parameter on the LHS. This study reviews the available work on parametric optimization, describes the challenges and issues specific to LHS parametric linear programming (LHS-pLP), and presents a solution algorithm using some classic results from matrix algebra. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： parametric programming Left-hand-side Uncertainty Linear program LP

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PERTURBATION ANALYSIS OF OPTIMIZATION PROBLEMS IN BANACH-SPACES

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NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION 1992年第1-2期13卷 97-116页

作者： SHAPIRO, A GEORGIA INST TECHNOL SCH IND & SYST ENGNATLANTAGA 30332

In this paper we study local behavior of optimal solutions of parametric programs in Banach spaces. A general approach to approximation of the original problem by a simpler one is outlined. Under various regularity co... 详细信息

关键词： NONLINEAR OPTIMIZATION parametric programming SENSITIVITY ANALYSIS LIPSCHITZ CONTINUITY DIRECTIONAL DERIVATIVE

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