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A quadratically convergent scaling Newton's method for nonlinear programming problems

Optimization 1998年第3期44卷 219-233页

作者： Lin, Zhenghua Song, Daicai Department of Mathematics Jilin University Changchun 130023 China Fushun Petroleum Institute Fushun 113001 China

Similar to [6], we present a W-quadratically convergent scaling Newton's method for nonlinear programming problems. At each iteration, the multiplier variables and slack variables generated by this algorithm all keep in positive orthant of R^m, we only compute a Newton step and determine the step length with at most 2 m division operations, where m is the number of constraints. In Section 4, three examples also support the Q-quadratic convergence. © 1998 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

关键词： Interior point algorithm nonlinear programming problem Q-quadratic convergence Scaling Newton's method

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Decomposition Method for nonlinear programming problems of Chemical Processes

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KAGAKU KOGAKU RONBUNSHU 2010年第5期36卷 512-518页

作者： Wakahara, Tatsuro Noda, Masaru Nishitani, Hirokazu Nara Inst Sci & Technol Grad Sch Informat Sci Ikoma Nara 6300192 Japan

Optimization problems of chemical process can generally be formulated as nonlinear programming problems, but the objective functions and the constraints of problems are often linear for most variables. In this paper, we propose a new decomposition method for nonlinear programming problems with two types of variables;linear and nonlinear variables. The proposed method is more effective than a nonlinear optimization method without decomposition to solve problems containing a relatively small number of nonlinear variables, because the dimension of the decomposed problem is much smaller than that of the original problem. Some computational results for the Rosen-Suzuki test problem indicate that the proposed method is useful for reducing the computational time.

关键词： Chemical Process Optimization nonlinear programming problem Decomposition Method Rosen-Suzuki Test problem

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Topology optimization of supporting structure for seismic response reduction of an arch

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Science China(Technological Sciences) 2016年第6期59卷 852-861页

作者： MIYAZU Yuji OHSAKI Makoto TSUDA Seita Department of Architecture Hiroshima University Department of Architecture and Architectural Engineering Kyoto University Department of Design and Technology Okayama Prefectural University

A flexible supporting structure that reduces seismic response of an arch is proposed. Topology and cross-sectional areas of the supporting structure modeled as a truss structure are optimized through two steps of static and dynamic optimization problems. In the first step, a flexible supporting structure that has diagonal displacement at the top under horizontal load is obtained by solving static optimization problems. Then, in the second step, the cross-sectional area of the flexible member is optimized to minimize the seismic response acceleration of the arch evaluated by the complete quadratic combination(CQC) method. Time-history seismic response analysis is carried out to show that the response in the normal direction of the roof successfully decreases due to flexibility of the supporting structure; in addition, installing passive energy dissipation devices into the flexible supporting structure is very effective in reducing the tangential response of the arch.

关键词： topology optimization arch supporting structure truss nonlinear programming problem CQC method

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Estimation of more than one parameters in stratified sampling with fixed budget

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2012年第2期75卷 185-197页

作者： Varshney, Rahul Najmussehar Ahsan, M. J. Aligarh Muslim Univ Dept Stat & Operat Res Aligarh 202002 Uttar Pradesh India

In a multivariate stratified sampling more than one characteristic are defined on every unit of the population. An optimum allocation which is optimum for one characteristic will generally be far from optimum for others. A compromise criterion is needed to work out a usable allocation which is optimum, in some sense, for all the characteristics. When auxiliary information is also available the precision of the estimates of the parameters can be increased by using it. Furthermore, if the travel cost within the strata to approach the units selected in the sample is significant the cost function remains no more linear. In this paper an attempt has been made to obtain a compromise allocation based on minimization of individual coefficients of variation of the estimates of various characteristics, using auxiliary information and a nonlinear cost function with fixed budget. A new compromise criterion is suggested. The problem is formulated as a multiobjective all integer nonlinear programming problem. A solution procedure is also developed using goal programming technique.

关键词： Multivariate stratified sampling Compromise allocation nonlinear programming problem

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OPTIMALITY CONDITIONS VIA EXACT PENALTY FUNCTIONS

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SIAM JOURNAL ON OPTIMIZATION 2010年第6期20卷 3208-3231页

作者： Meng, K. W. Yang, X. Q. Hong Kong Polytech Univ Dept Appl Math Kowloon Hong Kong Peoples R China

In this paper, we study KKT optimality conditions for constrained nonlinear programming problems and strong and Mordukhovich stationarities for mathematical programs with complementarity constraints using l(p) penalty functions, with 0 <= p <= 1. We introduce some optimality indication sets by using contingent derivatives of penalty function terms. Some characterizations of optimality indication sets are obtained by virtue of the original problem data. We show that the KKT optimality condition holds at a feasible point if this point is a local minimizer of some l(p) penalty function with p belonging to the optimality indication set. Our result on constrained nonlinear programming includes some existing results from the literature as special cases.

关键词： KKT optimality condition nonlinear programming problem mathematical programs with complementarity constraints strong stationarity Mordukhovich stationarity exact penalty function

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Direct optimization of dynamic systems described by differential-algebraic equations

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OPTIMAL CONTROL APPLICATIONS & METHODS 2008年第6期29卷 445-466页

作者： Fabien, Brian C. Univ Washington Dept Mech Engn Seattle WA 98195 USA

This paper presents a method for the optimization of dynamic systems described by index-1 differential-algebraic equations (DAE). The class of problems addressed include optimal control problems and parameter identification problems. Here, the controls are parameterized using piecewise constant inputs on a grid in the time interval of interest. In addition, the DAE are approximated using a Rosenbrock-Wanner (ROW) method. In this way the infinite-dimensional optimal control problem is transformed into a finite-dimensional nonlinear programming problem (NLP). The NLP is solved using a sequential quadratic programming (QP) technique that minimizes the L,,, exact penalty function, using only strictly convex QP subproblems. This paper shows that the ROW method discretization of the DAE leads to (i) a relatively small NLP problem and (ii) an efficient technique for evaluating the function, constraints and gradients associated with the NLP problem. This paper also investigates a state mesh refinement technique that ensures a sufficiently accurate representation of the optimal state trajectory. Two nontrivial examples are used to illustrate the effectiveness of the proposed method. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： nonlinear optimal control parameter identification nonlinear programming problem Rosenbrock-Wanner method

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Determining Optimum Strata Boundaries and Sample Sizes for Skewed Population with Log- Normal Distribution

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2015年第5期44卷 1364-1387页

作者： Khan, M. G. M. Rao, Dinesh Ansari, A. H. Ahsan, M. J. Univ S Pacific Sch Comp Informat & Math Sci Suva Fiji Kejriwal Inst Management & Dev Studies Ranchi Bihar India Aligarh Muslim Univ Dept Stat & Operat Res Aligarh Uttar Pradesh India

The method of choosing the best boundaries that make strata internally homogenous as far as possible is known as optimum stratification. To achieve this, the strata should be constructed in such a way that the strata variances for the characteristic under study be as small as possible. If the frequency distribution of the study variable x is known, the optimum strata boundaries (OSB) could be obtained by cutting the range of the distribution at suitable points. If the frequency distribution of x is unknown, it may be approximated from the past experience or some prior knowledge obtained at a recent study. Many skewed populations have log-normal frequency distribution or may be assumed to follow approximately log-normal frequency distribution. In this article, the problem of finding the OSB and the optimum sample sizes within the stratum for a skewed population with log-normal distribution is studied. The problem of determining the OSB is redefined as the problem of determining optimum strata widths (OSW) and is formulated as a nonlinear programming problem (NLPP) that seeks minimization of the variance of the estimated population mean under Neyman allocation subject to the constraint that the sum of the widths of all the strata is equal to the range of the distribution. The formulated NLPP turns out to be a multistage decision problem that can be solved by dynamic programming technique. A numerical example is presented to illustrate the application and computational details of the proposed method. A comparison study is conducted to investigate the efficiency of the proposed method with other stratification methods, viz., Dalenius and Hodges' cum root f method, geometric method by Gunning and Horgan, and Lavallee-Hidiroglou method using Kozak's algorithm available in the literature. The study reveals that the proposed technique is efficient in minimizing the variance of the estimate of the population mean and is useful to obtain OSB for a skewed population with log-n

关键词： Dynamic programming technique Log-normal distribution Multistage decision problem nonlinear programming problem Optimum sample size Optimum stratification Stratified sampling Primary 62D05 Secondary 80M50

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Solutions for fuzzy matrix games

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2010年第3期60卷 399-410页

作者： Cevikel, Adem C. Ahlatcioglu, Mehmet Yildiz Tekn Univ Art & Sci Fac Dept Math Istanbul Turkey

In this paper, we deal with two-person zero-sum games with fuzzy payoffs and fuzzy goals. We have presented two models for studying two-person zero-sum matrix games with fuzzy payoffs and fuzzy goals. We assume that each player has a fuzzy goal for each of the payoffs. We obtained that the fuzzy relation approach and the max-min solution are equivalent. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Fuzzy goal Fuzzy payoff matrix Fuzzy relation Fuzzy quantity nonlinear programming problem Max-min solution Relaxation procedure Two-person zero-sum games

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Transformed orthogonal functions for solving infinite horizon fractional optimal control problems

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EUROPEAN JOURNAL OF CONTROL 2021年 59卷 13-28页

作者： Shahini, M. Mehrpouya, M. A. Gonbad Kavous Univ Fac Basic Sci Dept Math & Stat Gonbad Kavous Iran Tafresh Univ Dept Math Tafresh *** Iran

In the present paper, an efficient numerical method for solution of infinite horizon fractional optimal con-trol problems is investigated. The fractional derivative in such problems is considered in the Caputo sense. The methodology developed here, is based on utilizing transformed orthogonal functions to approximate the state and control functions directly. Thereby, the original problem is converted to a nonlinear pro-gramming problem which can be solved by the well-developed parameter optimization algorithms. While the present solution procedure provides good results and high rate of convergence is achieved, the infinite horizon fractional optimal control problem is solved on the original time interval of the problem, without transforming it to a finite one. Illustrative examples are included at the end and the effectiveness of the proposed methodology is demonstrated. (c) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved. In the present paper, an efficient numerical method for solution of infinite horizon fractional optimal con-trol problems is investigated. The fractional derivative in such problems is considered in the Caputo sense. The methodology developed here, is based on utilizing transformed orthogonal functions to approximate the state and control functions directly. Thereby, the original problem is converted to a nonlinear pro-gramming problem which can be solved by the well-developed parameter optimization algorithms. While the present solution procedure provides good results and high rate of convergence is achieved, the infinite horizon fractional optimal control problem is solved on the original time interval of the problem, without transforming it to a finite one. Illustrative examples are included at the end and the effectiveness of the proposed methodology is demonstrated. (c) 2021 European Control Association. Published by Elsevier Ltd. All rights reserved.

关键词： Fractional optimal control Orthogonal functions Infinite horizon problems Collocation methods nonlinear programming problem

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Optimal 3D trajectory generation in delivering missions under urban constraints for a flying robot

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INTELLIGENT SERVICE ROBOTICS 2017年第3期10卷 241-256页

作者： Lavaei, Abolfazl Atashgah, M. A. Amiri Univ Tehran Fac New Sci & Technol Flight Dynam & Control Tehran Iran

Interest in applying flying robots especially quadcopters for civil applications, in particular for delivering purposes, has dramatically grown in the recent years. In fact, since quadcopters are capable of vertical takeoff and landing, they can be widely employed for nearly any aerial task where a human presence is hazardous or response time is critical. In this regard, quadcopters come to be very beneficial in delivering packages;accordingly, generating an optimal flight trajectory plays a preponderant role for meeting this vision. This paper is concerned with generation of a time-optimal3Dpath for a quadcopter under municipal restrictions in delivering tasks. To this end, the flying robot's dynamics is first modeled through Newton-Euler method. Subsequently, the problem is formulated as a time-optimal control problem such that the urban constraints, which are safe-margins of high-rise buildings located throughout the course, are first modeled and then imposed to the trajectory optimization problem as inequality constraints. After discretizing the trajectory by means of Hermit-Simpson method, the optimal control problem is transformed into a nonlinear programming problem and finally is solved by the direct collocation technique. Extensive simulations demonstrate the efficacy of the proposed method and correspondingly verify the effectiveness of the suggested method in generation of optimum 3D routes while all constraints and mission requirements are satisfied.

关键词： Optimal 3D path generation 6DOF dynamics Direct collocation technique Hermit-Simpson method nonlinear programming problem

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