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Complementarity active-set algorithm for mathematical programming problems with equilibrium constraints

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2007年第3期134卷 467-481页

作者： Judice, J. J. Sherali, H. D. Ribeiro, I. M. Faustino, A. M. Univ Porto Dept Civil Engn Fac Engn Mat Sect P-4100 Oporto Portugal Univ Coimbra Dept Matemat P-3000 Coimbra Portugal Inst Telecommun Lisbon Portugal Grado Dept Ind & Syst Engn Virginia Polytech Inst Blacksburg VA USA Virginia State Univ Blacksburg VA USA

In this paper, an algorithm for solving a mathematical programming problem with complementarity (or equilibrium) constraints (MPEC) is introduced, which uses the active-set methodology while maintaining the complementarity restrictions throughout the procedure. Finite convergence of the algorithm to a strongly stationary point of the MPEC is established under reasonable hypotheses. The algorithm can be easily implemented by adopting any active-set code for nonlinear programming. Computational experience is included to highlight the efficacy of the proposed method in practice.

关键词： local optimization complementarity mathematical programming problem with equilibrium constraints active-set algorithm

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An active-set algorithm for support vector machines in nonlinear system identification

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IFAC Proceedings Volumes 2004年第13期37卷 351-356页

作者： Michael Vogt Vojislav Kecman Darmstadt University of Technology Institute of Automatic Control Landgraf-Georg-Strasse 4 64283 Darmstadt Germany University of Auckland School of Engineering Private Bag 92019 Auckland New Zealand

This contribution describes an active-set algorithm for the optimization of regression support vector machines (SVMs). Its intended use is mainly system identification. Currently, SVMs are computed solving a QP problem by working-set algorithms like the SMO method. Although showing good results in general, they may perform weakly in some situations, particularly when solving regression problems. In these cases, active-set techniques (which are robust general-purpose QP solvers) have been shown to be a reasonable alternative. The paper considers how to adapt them to SVM regession with fixed or variable bias term and applies them to the identification of a condensing boiler.

关键词： system identification regression nonlinear support vector machines quadratic programming active-set algorithm

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active set algorithm for mathematical programs with linear complementarity constraints

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APPLIED MATHEMATICS AND COMPUTATION 2011年第21期217卷 8291-8302页

作者： Yin, Hongxia Ding, Fei Zhang, Jianzhong Minnesota State Univ Mankato Dept Math & Stat Mankato MN 56001 USA Chinese Acad Sci Grad Univ CAS Res Ctr Fict Econ & Data Sci Beijing 100080 Peoples R China GuangDong Dev Bank Dept Risk Management Guangzhou 510080 Guangdong Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China

In the paper, an incomplete active set algorithm is given for mathematical programs with linear complementarity constraints (MPLCC). At each iteration, a finite number of inneriterations are contained for approximately solving the relaxed nonlinear optimization problem. If the feasible region of the MPLCC is bounded, under the uniform linear independence constraint qualification (LICQ), any cluster point of the sequence generated from the algorithm is a B-stationary point of the MPLCC. Preliminary numerical tests show that the algorithm is promising. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Mathematical programs with linear complementarity constraints active-set algorithm B-stationary Uniform LICQ Convergence

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Gudermannian neural networks using the optimization procedures of genetic algorithm and active set approach for the three-species food chain nonlinear model

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JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2022年第7期14卷 8913-8922页

作者： Sabir, Zulqurnain Ali, Mohamed R. Sadat, R. Hazara Univ Dept Math & Stat Mansehra Pakistan Future Univ Fac Engn & Technol Cairo Egypt Benha Univ Fac Engn Benha Dept Basic Sci Banha 13512 Egypt Zagazig Univ Fac Engn Dept Phys & Engn Math Zagazig Egypt

The present study is to investigate the Gudermannian neural networks (GNNs) using the optimization procedures of genetic algorithm and active-set approach (GA-ASA) to solve the three-species food chain nonlinear model. The three-species food chain nonlinear model is dependent upon the prey populations, top-predator, and specialist predator. The design of an error-based fitness function is presented using the sense of the three-species food chain nonlinear model and its initial conditions. The numerical results of the model have been obtained by exploiting the GNN-GA-ASA. The obtained results through the GNN-GA-ASA have been compared with the Runge-Kutta method to substantiate the correctness of the designed approach. The reliability, efficacy and authenticity of the proposed GNN-GA-ASA are examined through different statistical measures based on single and multiple neurons for solving the three-species food chain nonlinear model.

关键词： Gudermannian neural network Three-dimensional food chain nonlinear model Nonlinear differential system Runge-Kutta scheme active-set algorithm Statistical studies

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A complementarity-based partitioning and disjunctive cut algorithm for mathematical programming problems with equilibrium constraints

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JOURNAL OF GLOBAL OPTIMIZATION 2006年第1期36卷 89-114页

作者： Judice, Joaquim J. Sherali, Hanif D. Ribeiro, Isabel M. Faustino, Ana M. Univ Coimbra Dept Matemat P-3000 Coimbra Portugal Inst Telecomunicacoes Coimbra Portugal Virginia Polytech Inst & State Univ Grado Dept Ind & Syst Engn Blacksburg VA 24061 USA Univ Porto Fac Engn Dept Civil Engn Seccao Matemat P-4100 Oporto Portugal

In this paper a branch-and-bound algorithm is proposed for finding a global minimum to a Mathematical Programming Problem with Complementarity (or Equilibrium) Constraints (MPECs), which incorporates disjunctive cuts for computing lower bounds and employs a Complementarity active-set algorithm for computing upper bounds. Computational results for solving MPECs associated with Bilivel Problems, NP-hard Linear Complementarity Problems, and Hinge Fitting Problems are presented to highlight the efficacy of the procedure in determining a global minimum for different classes of MPECs.

关键词： active-set algorithm branch-and-bound method complementarity disjunctive cuts global optimization

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Optimizing the selection and scheduling of multi-class projects using a Stackelberg framework

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2020年第2期286卷 508-522页

作者： Miralinaghi, Mohammad Seilabi, Sania E. Chen, Sikai Hsu, Yu-Ting Labi, Samuel Purdue Univ Lyles Sch Civil Engn 550 Stadium Mall Dr W Lafayette IN 47907 USA Purdue Univ CCAT NEXTRANS Ctr 550 Stadium Mall Dr W Lafayette IN 47907 USA Natl Taiwan Univ Dept Civil Engn Room 305Civil Engn Bldg 1Sec 4Roosevelt Rd Taipei 10617 Taiwan

One of the major causes of non-recurrent traffic congestion in urban areas is the implementation of transport infrastructure projects on city roads. The seeming ubiquity of work zones in cities causes road user frustration and safety hazards, and public relations problems for the transport agency. For this reason, transport agencies seek strategic ways to not only select urban projects but also schedule them in a manner that minimizes the effort associated with these functions. In other words, they seek to exploit the synergies between the tasks of project selection and project scheduling while duly accommodating the project interdependencies. This study introduces a general framework that simultaneously and optimally selects and schedules urban road projects subject to budgetary constraints over a given planning horizon. The project classes considered in this study are lane addition, new road construction, and road maintenance. Through a mimicry of the classic Stackelberg leader-follower game, this problem is formulated herein as a bi-level program. In the upper level, the leader (transport agency decision-makers) determines an optimal set of projects from a larger pool of candidate projects and decides an optimal schedule for their implementation. In the lower level, the followers (road users) seek to minimize their travel delays based on the two decisions made by the leader in the upper level. The numerical experiments show that if the decision-makers do not consider the peri-implementation capacity reduction, the resulting set of selected projects and their construction schedule can lead to significant travel delay cost for the road users. (C) 2020 Elsevier B.V. All rights reserved.

关键词： Transport Project selection Project scheduling Bi-level program active-set algorithm

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Swarming Computational Approach for the Heartbeat Van Der Pol Nonlinear System

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Computers, Materials & Continua 2022年第9期72卷 6185-6202页

作者： Muhammad Umar Fazli Amin Soheil Salahshour Thongchai Botmart Wajaree Weera Prem Junswang Zulqurnain Sabir Department of Mathematics and Statistics Hazara UniversityMansehraPakistan Faculty of Engineering and Natural Sciences Bahcesehir UniversityIstanbulTurkey Department of Mathematics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand Department of Statistics Faculty of ScienceKhon Kaen UniversityKhon Kaen40002Thailand

The present study is related to design a stochastic framework for the numerical treatment of the Van der Pol heartbeat model(VP-HBM)using the feedforward artificial neural networks(ANNs)under the optimization of particle swarm optimization(PSO)hybridized with the active-set algorithm(ASA),i.e.,*** global search PSO scheme and local refinement of ASA are used as an optimization procedure in this *** error-based merit function is defined using the differential VP-HBM form as well as the initial *** optimization of the merit function is accomplished using the hybrid computing performances of *** designed performance of ANNs-PSO-ASA is implemented for the numerical treatment of the VP-HBM dynamics by fluctuating the pulse shape adjustment terms,external forcing factor and damping coefficient with fixed ventricular contraction *** perform the correctness of the present scheme,the obtained numerical results through the designed ANN-PSO-ASA will be compared with the Adams numerical *** statistical investigations with larger dataset are provided using the“mean absolute deviation”,“Theil’s inequality coefficient”and“variance account for”operators to perform the applicability,reliability,and effectiveness of the designed ANNs-PSO-ASA scheme for solving the VP-HBM.

关键词： Particle swarm optimization van der Pol heartbeat system statistical analysis artificial neural networks active-set algorithm numerical computing

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Numerical treatment of nonlinear singular Flierl-Petviashivili systems using neural networks models

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NEURAL COMPUTING & APPLICATIONS 2019年第7期31卷 2371-2394页

作者： Raja, Muhammad Asif Zahoor Khan, Junaid Ali Zameer, Aneela Khan, Najeeb Alam Manzar, Muhammad Anwaar COMSATS Inst Informat Technol Dept Elect Engn Attock Pakistan HITEC Univ Texila Dept Comp Sci & Engn Rawalpindi Pakistan Pakistan Inst Engn & Appl Sci Dept Comp & Informat Sci Islamabad Pakistan Univ Karachi Dept Math Sci Karachi 75270 Pakistan Hamdard Univ Hamdard Inst Engn & Technol Islamabad Pakistan

In this study, new intelligent computing methodologies have been developed for highly nonlinear singular Flierl-Petviashivili (FP) problem having boundary condition at infinity by exploiting three different neural network models integrated with active-set algorithm (ASA). A modification in the modeling is introduced to cater the singularity, avoid divergence in results for unbounded inputs and capable of dealing with strong nonlinearity. Three models have been constructed in an unsupervised manner for solving the FP equation using log-sigmoid, radial basis and tan-sigmoid transfer functions in the hidden layers of the network. The training of adaptive adjustable variables of each model is carried out with a constrained optimization technique based on ASA. The proposed models have been evaluated on three variants of the two FP equations. The designed models have been examined with respect to precision, stability and complexity through statistics.

关键词： Flierl-Petviashivili problem Artificial neural networks Radial basis function Nonlinear ODEs Nonlinear singular systems active-set algorithm

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Thermal optimization of a single inlet T-junction

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INTERNATIONAL JOURNAL OF THERMAL SCIENCES 2012年 53卷 108-118页

作者： Bornschlegell, A. S. Pelle, J. Harmand, S. Bekrar, A. Chaabane, S. Trentesaux, D. Univ Lille Nord France F-59000 Lille France TEMPO UVHC F-59313 Valenciennes France

We present the thermal optimization study of a single inlet 90 T-junction. Head losses in association with the lumped method are used to calculate the 2D temperature field from a specific geometrical configuration, heat sources, boundary conditions and available ventilation power. This simple case is used as a benchmark to show a possible optimization methodology and to test 4 optimization algorithms suitable to non-linear problems;they are the active-set, Interior Point, Genetic algorithm and Particle Swarm Optimization. The optimization problem is defined by an Aggregated Objective Function (AOF) that depends on three geometrical parameters which are subjected to linear and non-linear constraints. In order to consider not only the global thermal behavior, but also local hotspots, the AOF combines mean solid temperature pondered by its volume and the maximal temperature. Five weights for these criteria were tested. The physical interpretation of different points helped to identify the optimal geometrical characteristics. All optimization algorithms demonstrated to be able to avoid local minima with this benchmark, if properly used. (C) 2011 Elsevier Masson SAS. All rights reserved.

关键词： T-junction Lumped method Non-linear thermal optimization active-set algorithm Genetic algorithm Particle Swarm Optimization

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Optimal control of network flows with convex cost and state constraints

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OPTIMAL CONTROL APPLICATIONS & METHODS 2000年第1期21卷 21-45页

作者： Ernst, AT Goh, CJ Univ Western Australia Dept Math Nedlands WA 6009 Australia

Consider a network in which a commodity flows at a variable rate across the arcs in order to meet supply/demand at the nodes, The aim is to optimally control the rate of flow such that a convex objective functional is minimized. This is an optimal control problem with a large number of states, and with an even larger number of controls. It is also complicated by storage bounds at the nodes leading to two state constraints for each node, We show, under some mild assumptions on the problem's parameters, that an exact solution to this state-constrained optimal control problem can be found efficiently without a complete discretization of the time variable, and develop a solution algorithm, based on the active-set-on-a-graph (ASG) algorithm for static convex flow problems. A brief description of a possible application as well as some numerical results are provided to illustrate the usefulness of the algorithm. Copyright (C) 2000 John Wiley & Sons, Ltd.

关键词： state constraints convex network optimization active-set algorithm water distribution

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