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Implementation of a robust SQP algorithm

OPTIMIZATION METHODS & SOFTWARE 2008年第6期23卷 827-846页

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

This paper presents an implementation of a sequential quadratic programming (SQP) algorithm for the solution of nonlinear programming (NLP) problems. In the proposed algorithm, a solution to the NLP problem is found by minimizing the L1 exact penalty function. The search direction for the penalty function minimization is determined by solving a strictly convex quadratic programming (QP) problem. Here, we make the basic SQP algorithm more robust (i) by solving a relaxed, strictly convex, QP problem in cases where the constraints are inconsistent, (ii) by performing a non-monotone line search to improve efficiency, and (iii) by using second-order corrections to avoid the Maratos effect. The robustness of the algorithm is demonstrated via a C language implementation that is applied to numerous parameter optimization and optimal control problems that have appeared in the literature. The results obtained show that both non-monotone line searches and second-order corrections can significantly reduce the amount of work required to solve parameter optimization problems.

关键词： nonlinear programming problem sequential quadratic programming computer code

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Modeling Complex Telecom Investments: A System of Systems Approach

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IEEE TRANSACTIONS ON ENGINEERING MANAGEMENT 2015年第4期62卷 631-642页

作者： Tsilipanos, Kosmas Neokosmidis, Ioannis Varoutas, Dimitris Univ Athens Fac Informat & Telecommun GR-15784 Athens Greece Consulting Soc Responsabilite Limitee SARL INCITES L-8008 Strassen Luxembourg

This paper presents a complex telecom investment problem analysis using system of systems concepts. This is necessary due to problem's multidimensional nature with several interdependences, and the presence of uncertainty and competition. A genetic algorithm is implemented in MATLAB in order to optimize the objective function (operator's profitability) of the formulated nonlinear programming problem. This approach is capable of providing optimal policies (regarding, e.g., services pricing, inception of investment, or revenues reinvestment) in a competitive market helping future investors in decision making by using various emulated strategic plans as reference.

关键词： Genetic algorithms (GAs) investment nonlinear programming problem optimization policy system of systems techno-economic telecommunications

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Human Motion Synthesis Using Trigonometric Splines

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IEEE ACCESS 2023年 11卷 14293-14308页

作者： Zhakatayev, Altay Avazov, Nurilla Rogovchenko, Yuriy Patzold, Matthias Univ Agder Dept ICT N-4604 Kristiansand Norway Univ Agder Dept ICT N-4879 Grimstad Norway Univ Agder Dept Math N-4604 Kristiansand Norway

In this work, we present a simple framework to synthesize human motion. Our main goal is to propose a methodology tailored for inexperienced users to initiate their research in human motion simulation and human motion trajectory optimization. The novelties of the work include the following. First, trigonometric splines are used instead of traditional B-splines to discretize the generalized coordinates and velocities. Second, useful identities for trigonometric splines are derived. Third, this work is intended to be an example, so that even non-skilled users, such as undergraduate students, can perform human motion analysis using a high-level programming language such as MATLAB. Four simulations of human motion are generated: walking, sitting and standing, side-step, and jump. The results of the walking simulation are validated by experiments. Simulation and experimental results are presented and discussed.

关键词： Splines (mathematics) Optimization Mathematical models Dynamics Biological system modeling Computational modeling Legged locomotion Human motion synthesis nonlinear programming problem trigonometric splines trajectory optimization

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On fuzzy TOPSIS method based on alpha level sets

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2017年第6期33卷 4067-4076页

作者： Wang, Weize Guangxi Normal Univ Sch Econ & Management Yucai Rd Qixing Dist 541004 Guilin Peoples R China

In a paper by Wang and Elhag [Ying-Ming Wang and Taha M.S. Elhag, Fuzzy TOPSIS method based on alpha level sets with an application to bridge risk assessment, Expert Systems with Applications 31 (2006) 309-319], a fuzzy TOPSIS method on alpha level sets was introduced and a nonlinear programming solution procedure was presented. It is found that in the case that the fuzzy decision matrix is of the same dimension and needs no normalization, a pair of nonlinear programming models is incorrect for computing the relative closeness provided by the above paper. In this paper we present a correct pair of nonlinear programming models in the case of the same dimension and justify it from the viewpoint of monotonic function. An illustrated example for selecting the best supplier of metallic components used in a variety of transmission cables has been examined using the proposed programming models to fuzzy TOPSIS method and demonstrated its superiorities, rationalities.

关键词： nonlinear programming problem TOPSIS fuzzy multiple criteria decision making fuzzy weighted average alpha level sets

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Modelling input parameter interactions in the possibilistic harmonic load flow

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IET GENERATION TRANSMISSION & DISTRIBUTION 2012年第6期6卷 528-538页

作者： Romero, A. A. Zini, H. C. Ratta, G. Univ Nacl San Juan Inst Energia Elect San Juan Argentina

In a previous study by the authors, a possibilistic harmonic load flow (PHLF) approach was presented. The PHLF was capable of modelling, through possibility distributions, uncertainties regarding magnitude and composition in both linear (LL) and non-linear loads (NLL) connected at the power system (PS). However, in that approach, possibility non-interaction between parameters for modelling LL and NLL was assumed. Such assumption is quite conservative and conduces to uncertainty overestimation. In fact, there are well-defined physical relationships among model parameters that constrain the variability of these. This study presents an improved approach which overcomes the aforementioned drawback by including both linear and non-linear equality constraints into the non-linear programming problem used to compute the PHLF. These linear and non-linear equality constraints are specifically used to model the balance of active and reactive power, respectively, at each bus of the PS. The equality constrains inclusion is supported from a possibility theory point of view by means of the 'information fusion concept'. Influence of the possibility interaction consideration is evaluated in the IEEE 14-bus PS for harmonic analysis. Then, the complete PHLF is tested in a real 88-bus PS, and comparisons with Monte Carlo simulation results are performed and discussed.

关键词： possibilistic harmonic load flow PHLF approach Optimisation techniques power system harmonics linear equality constraints nonlinear programming equality constraint inclusion nonlinear equality constraints harmonic analysis Power supply quality and harmonics nonlinear programming problem uncertainty overestimation linear loads reactive power Monte Carlo methods input parameter interaction modelling possibility theory point of view active power information fusion concept nonlinear loads Monte Carlo simulation load flow Power systems

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Probabilistic undervoltage load shedding using point estimate method

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IET GENERATION TRANSMISSION & DISTRIBUTION 2015年第15期9卷 2234-2244页

作者： Kaffashan, Iman Amraee, Turaj KN Toosi Univ Technol Fac Elect Engn Tehran Iran

Undervoltage load shedding (UVLS) is executed as a last resort to avoid voltage instability in critical situations. In this study, a robust UVLS scheme based on the point estimate method (PEM) is developed taking load uncertainties into consideration. The utilised PEM converts the continuous probability distribution functions (PDFs) of load uncertainty to discrete statistical moments. The extracted moments could represent the behaviours of original continuous PDFs. The proposed stochastic UVLS strategy is expressed as a non-linear programming problem, which is optimised using sequential quadratic programming technique. The fulfilment of the suggested scheme is compared with Monte Carlo simulation technique for two IEEE 14-bus and IEEE 118-bus test grids.

关键词： load shedding statistical distributions stochastic processes nonlinear programming quadratic programming probabilistic undervoltage load shedding point estimate method robust UVLS scheme PEM load uncertainties continuous probability distribution functions PDF discrete statistical moments stochastic UVLS strategy nonlinear programming problem sequential quadratic programming technique IEEE 14-bus test grid IEEE 118-bus test grid

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Optimal control problem of multi-vehicle cooperative autonomous parking trajectory planning in a connected vehicle environment

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IET INTELLIGENT TRANSPORT SYSTEMS 2019年第11期13卷 1677-1685页

作者： Wu, Bing Qian, Lijun Lu, Meiling Qiu, Duoyang Liang, Haiqin Hefei Univ Technol Coll Automot & Transportat Engn Dept Vehicle Engn Hefei 230009 Anhui Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Automat Engn Dept Elect Engn Nanjing 210016 Jiangsu Peoples R China

The development of intelligent network and intelligent vehicle technology makes it possible for multi-vehicle cooperative driving. In this study, the multi-vehicle cooperative autonomous parking condition is addressed by establishing a vehicle kinematics model combined with dynamic constraints and endpoint and collision avoidance constraints. The autonomous parking trajectory planning problem is transformed into an optimal control problem. The shortest parking completion time is set as the optimal cost function, and the optimal control problem is discretised by using the Gauss pseudo-spectral method. Then, the non-linear programming problem is solved. Moreover, an initial guess generation strategy is proposed, and the iteration method is used to solve the problem by adding collision avoidance constraints to the collision situation of the vehicle to improve the convergence and robustness of the problem. The simulation model is built in MATLAB/Simulink to simulate multi-vehicle cooperative autonomous parking under different working conditions. The simulation results show that the proposed method can solve the multi-vehicle cooperative autonomous parking trajectory planning problem uniformly and effectively. Compared with the traditional pseudo-spectral method, the proposed method has a faster convergence speed.

关键词： optimisation nonlinear programming path planning iterative methods optimal control mathematics computing mobile robots collision avoidance trajectory control linear programming optimal control problem connected vehicle environment intelligent vehicle technology autonomous parking condition vehicle kinematics model collision avoidance constraints autonomous parking trajectory planning problem shortest parking completion time optimal cost function nonlinear programming problem

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Minimax theorems and its applications in locally convex subsets of banach manifolds

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nonlinear ANALYSIS-THEORY METHODS & APPLICATIONS 1996年第2期27卷 187-205页

作者： Wang, TX Department of Mathematics The University of Connecticut Groton CT 06340 U.S.A.

The von Neumann minimax theorem has been applied in many areas and there are many extensions of the theorem. In Shi and Chang (1985) the theorem is generalized to a form in which a compactness condition of sets was replaced by a compactness condition of the function. The main aim of the paper is to extend Shi and Chang's result from convex sets to locally convex sets. First, a frame of variational methods on locally convex closed subsets of Banach manifolds is established. Lop-sided minimax theorem are next proven on locally convex closed subsets of Banach manifolds. Based on the lop-sided minimax theorem the proof of the main theorem is given. As applications of these theorems, a generalized Ky Fan's inequality is given as well as an existence theorem of equilibria in game theory. Finally a proof is given of an existence theorem for a solution of nonlinear programming problems which generalizes theorem 4.3 in Shi and Chang (1985).

关键词： Ky Fan's inequality locally convex subset lop-sided minimax theorem Nash equilibria nonlinear programming problem relative critical point relatively differential function

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Extended ADMMs for RPO of large-scale power systems with discrete controls

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第11期12卷 2624-2632页

作者： Zheng, Jiabin Liu, Mingbo Lu, Wentian Xie, Min Zhu, Jianquan South China Univ Technol Sch Elect Power Engn Guangzhou Guangdong Peoples R China

The reactive power optimization (RPO) problem of power systems is a mixed-integer nonlinear programming problem, which can be computationally expensive. This paper applies the alternating direction method of multipliers (ADMM) to solve it. By duplicating discrete control variables with one copy allowed to vary continuously, the RPO model is formulated as a modified model in which the objective function and constraints have a separable structure with respect to the continuous and discrete variables, except for the coupling constraint. We then applied the ADMM to solve this model with the separable structure, and hence the original problem is converted into two optimization sub-problems, which are nonlinear programming (NLP) and mixed-integer quadratic programming (MIQP) problems, respectively. To improve the convergence of the algorithm, we proposed an extended ADMM by adding the upper and lower limits on state variables into the MIQP sub-problem based on the sensitivities obtained in the NLP sub-problem. We also established a mechanism to filter out inactive inequality constraints in the MIQP sub-problem to improve computational speed. Moreover, numerical results tested on IEEE test systems and a real 739-bus system have shown the correctness of the proposed method and its adaptability for power systems with different sizes and configurations.

关键词： power system control reactive power control discrete systems quadratic programming integer programming extended ADMM method RPO problem large-scale power system reactive-power optimisation problem nonlinear programming problem nondeterministic polynomial-time hard alternating direction method of multiplier discrete control variable mixed-integer quadratic programming problem MIQP problem IEEE test system real 739-bus system

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An Optimization Approach for nonlinear programming problems with Interval Coefficients

An Optimization Approach for Nonlinear Programming Problems ...

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2015 4th International Conference on Computer, Mechatronics, Control and Electronic Engineering (ICCMCEE 2015)

作者： Mei Ma Hecheng Li Department of Mathematics Qinghai Normal University

ISBN: (纸本)9781510813465

When some coefficients involved in nonlinear programming problems are taken as interval numbers, the problem becomes more challengeable than the original one. In the paper, a nonlinear programming problem with interval objective coefficients is considered, and a genetic algorithm is presented. Firstly, the original problem is transformed into a bilevel programming model without interval coefficients. In addition, a genetic algorithm is designed and used to deal with the transformed problem, in which the search space is decided by these intervals given in the original problem. Based on the proposed approach, the best and the worst optimal solutions as well as some intermediate solutions can be obtained. Finally, a computational example is solved and the results show that the proposed algorithm is efficient and robust.

关键词： nonlinear programming problem interval coefficients bilevel program

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