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Multiplier Methods for Optimization problems with Lipschitzian Derivatives

COMPUTATIONAL MATHEMATICS AND mathematical PHYSICS 2012年第12期52卷 1603-1611页

作者： Izmailov, A. F. Kurennoy, A. S. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119992 Russia

Optimization problems for which the objective function and the constraints have locally Lipschitzian derivatives but are not assumed to be twice differentiable are examined. For such problems, analyses of the local convergence and the convergence rate of the multiplier (or the augmented Lagrangian) method and the linearly constraint Lagrangian method are given. DOI: 10.1134/S0965542512120081

关键词： mathematical programming problem augmented Lagrangian multiplier method linearized constraints Newtonian iterative scheme

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Programmable Logic Controller for Embedded Implementation of Input-Constrained Systems

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IFAC-PapersOnLine 2017年第1期50卷 14412-14417页

作者： Levenson, Richard M. Nelson, Zachary E. Adegbege, Ambrose A. Department of Electrical and Computer Engineering The College of New Jersey EwingNJ08628-0718 United States Department of Electrical and Computer Engineering The Johns Hopkins University BaltimoreMD21218 United States

Programmable logic controllers (PLCs) have the benefit of being able to withstand a variety of environments while maintaining high reliability compared to computers and other controllers. Traditionally, PLCs have been used for simple ON-OFF control schemes or for proportional-integral-derivative (PID) control. However, recent developments in technology have allowed even low-cost PLCs to implement more advanced and efficient algorithms. This paper investigates a PLC implementation of the specialized Projected Gauss-Seidel (PGS) algorithm. The PGS algorithm is able to quickly and efficiently solve both symmetric and asymmetric mathematical programming problems. The algorithm can be further utilized to solve more complicated problems such as model predictive control (MPC). The focus of this paper is to solve a general constrained optimization problem on a PLC and to expand the capability to solve a MPC example. The DirectLogic Do-More PLC is exploited both for computational efficiency and for memory utilization. © 2017

关键词： Controllers Computation theory Computational efficiency Computer circuits Constrained optimization Embedded systems mathematical programming Model predictive control Predictive control systems problem solving Programmable logic controllers Programmed control systems Proportional control systems Two term control systems Embedded implementation Gauss Seidel General constrained optimization High reliability Input constrained systems mathematical programming problem Memory utilization Proportional integral derivative control

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Solution of the Two-Level Hierarchical Minimax Program Control problem in a Nonlinear Discrete-Time Dynamical System

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IFAC-PapersOnLine 2018年第13期51卷 579-584页

作者： Shorikov, Andrey F. Department of Applied Mathematics Ural Federal University 19 Mira str. Ekaterinburg620002 Russia

In this paper we consider a discrete-time dynamical system consisting of two controllable objects. The dynamics of each object is described by the corresponding nonlinear discrete-time vector recurrent equation. The quality of process implementation at each level of the control system is estimated by the corresponding terminal convex and differentiable functional. For the dynamical system under consideration, a mathematical formalization of a two-level hierarchical minimax program control problem in the presence of perturbations, and an algorithm for its solving are proposed. The construction of this algorithm can be implemented as a finite sequence of solutions of a linear and convex mathematical programming problems, and a finite discrete optimization problems. © 2018

关键词： Discrete time control systems Dynamical systems mathematical programming Nonlinear equations Quality control Discrete optimization problems Discrete time dynamical systems Finite sequence mathematical programming problem Minimax programs Nonlinear discrete time Process implementation Recurrent equations

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Solving the shortest path problem on networks with fuzzy arc lengths using the complete ranking method

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OPERATIONAL RESEARCH 2022年第4期22卷 3607-3631页

作者： Verma, Tina Thapar Inst Engn & Technol Sch Math Patiala 147004 Punjab India

The fuzzy shortest path problem provides the shortest way to the decision-maker having least possible distance from source to destination. Niroomand et al. (Oper Res 17:395-411, 2017) recently advanced a method for solving the fuzzy shortest path problem. They divided the problem into two sub-problems and solved them separately. They asserted that their method always meets a unique upper and lower bound on the fuzzy shortest distance from source to destination for each alpha. The proposed study focuses on a significant omission in Niroomand et al. method. The flaws in their approach stem from not clearly revealing the solution concept for the shortest path problem. The flaws of their approach are addressed in this study, and new approaches are proposed to over-come these flaws. The proposed approaches use the complete ranking method to solve the fuzzy shortest path problem. The proposed approaches ensure that the fuzzy shortest distance is equal among all possible shortest paths. The proposed research is carried out using numerical examples of fuzzy shortest path problems. The computational results of proposed approaches are compared to existing methods.

关键词： Shortest path Fuzzy mathematical programming problem Complete ranking method

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On the Influence of the Critical Lagrange Multipliers on the Convergence Rate of the Multiplier Method

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COMPUTATIONAL MATHEMATICS AND mathematical PHYSICS 2012年第11期52卷 1504-1519页

作者： Izmailov, A. F. Uskov, E. I. Moscow MV Lomonosov State Univ Fac Computat Math & Cybernet Moscow 119991 Russia

The paper is devoted to the analysis of the influence of the critical Lagrange multipliers on the convergence rate of the multiplier method and the efficiency of various techniques for accelerating the final stage of ... 详细信息

关键词： mathematical programming problem augmented Lagrangian method of multipliers superlinear convergence critical Lagrange multiplier stabilized Newton-Lagrange method

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Designing stratified sampling in economic and business surveys

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JOURNAL OF APPLIED STATISTICS 2015年第10期42卷 2080-2099页

作者： Khan, M. G. M. Reddy, K. G. Rao, D. K. Univ S Pacific Sch Comp Informat & Math Sci Suva Fiji

In most economic and business surveys, the target variables (e.g. turnover of enterprises, income of households, etc.) commonly resemble skewed distributions with many small and few large units. In such surveys, if a stratified sampling technique is used as a method of sampling and estimation, the convenient way of stratification such as the use of demographical variables (e.g. gender, socioeconomic class, geographical region, religion, ethnicity, etc.) or other natural criteria, which is widely practiced in economic surveys, may fail to form homogeneous strata and is not much useful in order to increase the precision of the estimates of variables of interest. In this paper, a stratified sampling design for economic surveys based on auxiliary information has been developed, which can be used for constructing optimum stratification and determining optimum sample allocation to maximize the precision in estimate.

关键词： economic survey stratified random sampling optimum stratification optimum sample size allocation mathematical programming problem dynamic programming technique

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Multiattribute decision analysis using strict preference relations

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ANNALS OF OPERATIONS RESEARCH 2016年第1-2期245卷 379-400页

作者： Nishizaki, Ichiro Hayashida, Tomohiro Ohmi, Masakazu Hiroshima Univ Grad Sch Engn Higashihiroshima 7398527 Japan

To identify multiattribute utility functions under the assumption of the mutual utility independence, a decision maker must specify indifference points and subjective probabilities precisely. By relaxing this rigorous evaluation, multiattribute value models with incomplete information have been developed. In this paper, we present a new method finding the best alternative through strict preference relations derived from the decision maker by asking questions that are relatively easy to answer compared to the indifference questions. In our method, alternatives consistent with the derived strict preference relations are obtained by solving mathematical programming problems with constraints representing the preference relations, and eventually we can find the most preferred alternative by deriving additional preference relations.

关键词： Multiattribute utility function Strict preference relation Incomplete information mathematical programming problem

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stratifyR: An R Package for optimal stratification and sample allocation for univariate populations

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AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS 2020年第3期62卷 383-405页

作者： Reddy, K. G. Khan, M. G. M. Australian Natl Univ Ctr Social Res & Methods Canberra ACT 2601 Australia Univ South Pacific Sch Comp Informat & Math Sci Suva Fiji

ThisRpackage determines optimal stratification of univariate populations under stratified sampling designs using a parametric-based method. It determines the optimum strata boundaries (OSB), optimum sample sizes (OSS) and multiple other quantities for the study variable,y, using the best-fit probability density function of a study variable available from survey data. The method requires the parameters and other characteristics of the distribution of the study variable to be known, either from available data or from a hypothetical distribution if the data are not available. In the implementation, the problem of determining the OSB is formulated as a mathematical programming problem and solved by using a dynamic programming technique. If the data of the population (i.e. the study variable) are available to the surveyor, the method estimates its best-fit distribution and determines the OSB and OSS under Neyman allocation, directly. When the dataset is not available, stratification is made based on the assumption that the values of the study variable,y, are available as hypothetical realisations of proxy values ofyfrom past/recent surveys. Thus, it requires certain distributional assumptions about the study variable. At present, the package handles stratification for the populations where the study variable follows a continuous distribution: namely, Pareto, Triangular, Right-triangular, Weibull, Gamma, Exponential, Uniform, Normal, Lognormal and Cauchy distributions. In this paper, applications of major functionalities in the package are illustrated with a number of real/simulated as well as some hypothetical populations.

关键词： dynamic programming mathematical programming problem optimum sample sizes optimum strata boundaries R project for statistical computing

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Algorithm for Solving of Two-Level Hierarchical Minimax Adaptive Control problem in a Linear Discrete-Time Dynamical System

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IFAC-PapersOnLine 2018年第32期51卷 838-843页

作者： Shorikov, Andrey F. Department of Applied Mathematics Ural Federal University 19 Mira str. Ekaterinburg620002 Russia

In this paper we consider a discrete-time dynamical system consisting from two controllable objects. The dynamics of each object is described by the corresponding vector linear discrete-time recurrent relation. In this dynamical system there are two levels of control. The quality of process implementation at each level of the control system is estimated by the corresponding terminal linear functional. For the dynamical system under consideration, a mathematical formalization of a two-level hierarchical minimax adaptive control problem in the presence of perturbations, and an algorithm for its solving are proposed. The construction of this algorithm can be implemented as a finite sequence of solutions of a linear mathematical programming problems, and a finite discrete optimization problems. © 2018

关键词： Discrete time control systems Adaptive control systems Dynamical systems mathematical programming Quality control Adaptive Control Algorithm for solving Discrete optimization problems Discrete time dynamical systems Linear functional mathematical programming problem Process implementation Recurrent relation

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OPTIMAL CONTROL OF SWITCHED IMPULSIVE SYSTEMS WITH TIME DELAY

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ANZIAM JOURNAL 2012年第4期53卷 292-307页

作者： Wong, K. H. Tang, W. M. Chongqing Normal Univ Coll Comp & Informat Sci Chongqing 400047 Peoples R China

We develop a computational method for solving an optimal control problem governed by a switched impulsive dynamical system with time delay. At each time instant, only one subsystem is active. We propose a computational method for solving this optimal control problem where the time spent by the state in each subsystem is treated as a new parameter. These parameters and the jump strengths of the impulses are decision parameters to be optimized. The gradient formula of the cost function is derived in terms of solving a number of delay differential equations forward in time. Based on this, the optimal control problem can be solved as an optimization problem.

关键词： switched and impulsive systems time delay subsystems magnitudes of impulses duration times mathematical programming problem

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