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

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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The positiveness of lower limits of the Hoffman constant in parametric polyhedral programs

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JOURNAL OF GLOBAL OPTIMIZATION 2012年第4期53卷 641-661页

作者： Jourani, A. Zagrodny, D. Polish Acad Sci Syst Res Inst PL-01447 Warsaw Poland Univ Bourgogne CNRS UFR Sci & Tech Inst Math BourgogneUMR 5584 F-21078 Dijon France Cardinal Stefan Wyszynski Univ Coll Sci Fac Math & Nat Sci PL-01815 Warsaw Poland

If K(t) are sets of admissible solutions in parametric programs then it is natural to ask about the Lipschitz-like property and the lower semi-continuity of the multifunction. Answers to this question are related to the problem of the continuity or Lipschitz continuity of the value function, namely having the lower semi-continuity of K(center dot) we get the upper semi-continuity of the function easily and the Lipschitz-like property of K(center dot) leads to the Lipschitz-continuity of it. Herein sufficient conditions to get these properties of the polyhedral multifunction of admissible solutions are given in terms of the lower limit of the Hoffman constant. It is shown that the multifunction is Lipschitz-like at these parameters at which the lower limit of the Hoffman constant are positive.

关键词： parametric programming Hoffman constant Error bound Mosco convergence Attouch's theorem Convex functions Subdifferentials Polyhedrals

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Inf-sup control of discontinuous piecewise affine systems

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2009年第13期19卷 1471-1492页

作者： Spjotvold, J. Kerrigan, E. C. Mayne, D. Q. Johansen, T. A. Norwegian Univ Sci & Technol Dept Engn Cybernet N-7491 Trondheim Norway Univ London Imperial Coll Sci Technol & Med Dept Aeronaut London SW7 2AZ England Univ London Imperial Coll Sci Technol & Med Dept Elect & Elect Engn London SW7 2AZ England

This paper considers the worst-case optimal control of discontinuous piecewise affine (PWA) systems, which are subjected to constraints and disturbances. We seek to pre-compute, via dynamic programming, an explicit control law for these systems when a PWA cost function is utilized. One difficulty with this problem class is that, even for initial states for which the value function of the optimal control problem is finite, there might not exist a control law that attains the infimum. Hence, we propose a method that is guaranteed to obtain a sub-optimal Solution, and where the degree Of sub-optimality can be specified a priori. This is achieved by approximating the underlying sub-problems with a parametric piecewise linear program. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： optimal control piecewise affine systems parametric programming approximate solutions to inf-sup problems

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SENSITIVITY ANALYSIS OF PARAMETRIZED PROGRAMS VIA GENERALIZED EQUATIONS

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1994年第2期32卷 553-571页

作者： SHAPIRO, A Georgia Institute of Technology Atlanta GA United States

This paper investigates local behavior of optimal solutions of parametrized optimization problems with cone constraints in Banach spaces. The corresponding first-order optimality conditions are formulated in a form of generalized equations (variational inequalities) and solutions of these generalized equations are studied. It is shown that under certain second-order sufficient optimality conditions and a regularity assumption related to the associated Lagrange multipliers, the considered optimal solutions are Lipschitzian stable. This is compared with a similar result in Shapiro and Bonnans [SIAM J. Control Optim., 30 (1992), pp. 1409-1422]. Under the additional assumption of uniqueness of the Lagrange multipliers, first-order expansions of the optimal solutions are given in terms of solutions of auxiliary optimization problems. Finally, as an example, semi-infinite programming problems are discussed.

关键词： NONLINEAR OPTIMIZATION parametric programming SENSITIVITY ANALYSIS GENERALIZED EQUATIONS LIPSCHITZIAN STABILITY DIRECTIONAL DIFFERENTIABILITY SEMIINFINITE programming

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Semiglobal stabilization of linear systems using constrained controls:: A parametric optimization approach

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 1999年第8期9卷 461-484页

作者： Solís-Daun, J Alvarez-Ramírez, J Suárez, R Univ Autonoma Metropolitana Iztapalapa Div Ciencias Basicas & Ingn Mexico City 09340 DF Mexico

A bounded feedback control for asymptotic stabilization of linear systems is derived. The designed control law increases the feedback gain as the controlled trajectory converges towards the origin. A sequence of invariant sets of decreasing size, associated with a (quadratic) Lyapunov function, are defined and related to each of them, the corresponding possible highest gain is chosen, while maintaining the input bounded. Gains as functions of the position are designed by explicitly solving a c-parameterized programming problem. The proposed method allows global asymptotic stabilization of open-loop stable systems, with inputs subject to magnitude bounds and globally bounded rates. In the general case of linear systems that are asymptotic null controllable with bounded input, the semiglobal stabilization is also addressed taking into account the problem of semiglobal rate-limited actuators. The method is illustrated with the global stabilization of an inertial navigator, and the stabilization of a nonlinear model of a crane with hanging load. Copyright (C) 1999 John Wiley & Sons, Ltd.

关键词： bounded control linear systems semiglobal stabilization parametric programming

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On the consistency of aggregate production frontiers

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第1期172卷 326-333页

作者： Weill, L Univ Robert Schuman Inst Etud Polit F-67082 Strasbourg France

This paper investigates the consistency of efficiency frontier methods applied at the aggregate level. We estimate eight aggregate production frontiers on a sample of 93 countries, depending on three methodological choices for the specification of the frontier: the choice of the approach technique (stochastic frontier approach or data envelopment analysis), the specification of human capital as an input, and the nature of returns to scale. We observe some differences on the descriptive statistics of the distributions of the efficiency scores, but also a very high significant and positive correlation between scores rankings regardless of the methodological choices made. Our results tend then to suggest the consistency of the efficiency techniques at the aggregate level. (C) 2004 Elsevier B.V. All rights reserved.

关键词： data envelopment analysis parametric programming macroeconomic efficiency frontiers

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A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第17期64卷 4576-4591页

作者： Simonetto, Andrea Mokhtari, Aryan Koppel, Alec Leus, Geert Ribeiro, Alejandro Delft Univ Technol Dept Elect Engn Math & Comp Sci NL-2826 CD Delft Netherlands Univ Penn Dept Elect & Syst Engn Philadelphia PA 19104 USA

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of 1/h, where h is the sampling period. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves asO(h(2)), and in some cases asO(h(4)), which outperforms the state-of-the-art error bound of O(h) for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

关键词： Time-varying optimization non-stationary optimization parametric programming prediction-correction methods

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An approach to parametric nonlinear least square optimization and application to task-level learning control

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1997年第7期42卷 912-927页

作者： Gorinevsky, D UNIV TORONTO FAC APPL SCI & ENGN TORONTO ON CANADA

This paper considers a parametric nonlinear least square (NLS) optimization problem, Unlike a classical NLS problem statement, we assume that a nonlinear optimized system depends on two arguments: an input vector and a parameter vector, The input vector can be modified to optimize the system, while the parameter vector changes from one optimization iteration to another and is not controlled, The optimization process goal is to find a dependence of the optimal input vector on the parameter vector, where the optimal input vector minimizes a quadratic performance index, The paper proposes an extension of the Levenberg-Marquardt algorithm for a numerical solution of the formulated problem, The proposed algorithm approximates the nonlinear system in a vicinity of the optimum by expanding it into a series of parameter vector functions, affine in the input vector. In particular, a radial basis function network expansion is considered. The convergence proof for the algorithm is presented, The proposed approach is applied to task-level learning control of a two-link flexible arm, Each evaluation of the system in the optimization process means completing a controlled motion of the arm, In the simulation example, the controlled motions take only about 1.5 periods of the lowest eigenfrequency oscillations. The algorithm controls this strongly nonlinear oscillatory system very efficiently, Without any prior knowledge of the system dynamics, it achieves a satisfactory control of arbitrary arm motions after only 500 learning (optimization) iterations.

关键词： approximation convergence flexible manipulator learning control Levenberg-Marquardt optimization parametric nonlinear least squares parametric programming radial basis function network

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