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3rd international conference on Complementarity Problems

作者： Hamdouch, Y Marcotte, P Nguyen, S Univ Montreal DIRO Montreal PQ H3C 3J7 Canada Univ Montreal CRT Montreal PQ H3C 3J7 Canada

In a transit network involving vehicles with rigid capacities, we advocate the use of strategies for describing consumer behavior. At each boarding node, a user sorts the transit lines in decreasing order of preference, and boards the first vehicle in this list whose residual capacity is nonzero. Since a user's position in the queue varies from day to day, the delay experienced is stochastic. This leads to an equilibrium problem where, at a solution. users are assigned to strategies that minimize their expected delay. This situation is formulated as a variational inequality, whose cost mapping is discontinuous and strongly asymmetric, due to the priority of cur-rent passengers over incoming users. We prove that the solution set is nonempty and provide numerical results obtained by an efficient solution algorithm.

关键词： transit networks equilibrium assignment strategy hyperpath capacities priorities variational inequalities

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Echo-State Conditional variational Autoencoder for Anomaly Detection

Echo-State Conditional Variational Autoencoder for Anomaly D...

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international Joint conference on Neural Networks (IJCNN)

作者： Suh, Suwon Chae, Daniel H. Kang, Hyon-Goo Choi, Seungjin Pohang Univ Sci & Technol Dept Comp Sci & Technol 77 Cheongam Ro Pohang 37673 South Korea SK Telecom Access Network Lab Seoul South Korea

ISBN: (纸本)9781509006199

Anomaly detection involves identifying the events which do not conform to an expected pattern in data. A common approach to anomaly detection is to identify outliers in a latent space learned from data. For instance, PCA has been successfully used for anomaly detection. variational autoencoder (VAE) is a recently-developed deep generative model which has established itself as a powerful method for learning representation from data in a nonlinear way. However, the VAE does not take the temporal dependence in data into account, so it limits its applicability to time series. In this paper we combine the echo-state network, which is a simple training method for recurrent networks, with the VAE, in order to learn representation from multivariate time series data. We present an echo-state conditional variational autoencoder (ES-CVAE) and demonstrate its useful behavior in the task of anomaly detection in multivariate time series data.

关键词： Learning systems

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Convergence of a finite element approximation to a degenerate parabolic variational inequality with non-smooth data arising from American option valuation

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OPTIMIZATION METHODS & SOFTWARE 2010年第5期25卷 699-723页

作者： Wang, Guanghui Wang, Song Univ Western Australia Sch Math & Stat Crawley WA 6009 Australia Chinese Acad Meteorol Sci State Key Lab Severe Weather LaSW Beijing 100081 Peoples R China

This paper deals with the approximation of solutions to a degenerate variational inequality of parabolic type with a non-smooth final condition arising from American option pricing by the piecewise linear finite element method in space and an implicit time-stepping scheme. We show that the error of the approximation in a weighted Sobolev norm is of order O(h2/3+ t1/3) under some realistic regularity assumptions on the exact solution, where h and t denote the mesh parameters in space and time, respectively. Numerical examples are presented to confirm our theoretical results.

关键词： variational inequality complementarity problem finite element analysis error bounds American option pricing Black-Scholes equation non-smooth data degenerate parabolic partial differential equations

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Model Predictive Control for Discrete Fuzzy Systems via Iterative Quadratic programming

Model Predictive Control for Discrete Fuzzy Systems via Iter...

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IEEE international conference on Fuzzy Systems

作者： Arino, Carlos Perez, Emilio Querol, Andres Sala, Antonio Univ Jaume 1 D Ingn Sistemas Ind & Diseno Castellon de La Plana 12071 Spain Univ Politecn Valencia Inst Univ Automat & Informat Ind E-46022 Valencia Spain

ISBN: (纸本)9781479920723

Takagi-Sugeno fuzzy models are exact representations of nonlinear systems in a compact region. Guaranteed-cost linear matrix inequalities produce controllers which minimize a shape-independent bound on a quadratic cost;however, the controller has a fixed structure (possibly suboptimal), say a Parallel Distributed Compensator (PDC), and does not allow input saturation. By posing the problem as a Model Predictive Control one, the ideas of terminal set, terminal controller and feasible set can be used in order to improve the performance of usual guaranteed-cost controllers for Takagi-Sugeno systems via Quadratic programming. A Polya-based approach has been introduced in order to (conservatively) transform the invariant set problem into a polytopic one, as well as computing the controller feasibility region. The optimal controller is computed iteratively.

关键词： Discrete Takagi-Sugeno Fuzzy Models Invariant sets Contractive sets and Robust Stability

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programming Problems with a Large Number of Objective Functions

Programming Problems with a Large Number of Objective Functi...

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international conference on Numerical Methods and Applications

作者： Resteanu, Cornel Trandafir, Romica Natl Inst Res & Dev Informat 8-10 Averescu Ave Bucharest 011455 1 Romania Tech Univ Civil Engn Bucharest 020396 Romania

ISBN: (纸本)9783642184659

The paper treats the Multi-Objective programming problem with a large composite set of (linear and nonlinear) objective functions, the domain of feasible solutions being defined by a set of linear equalities/inequalities representing a large scale problem. One constructs a preferred solution i.e. a non-dominated solution chosen via extending the decision-making framework. A feasible approach, for this class of problems, is to use a solver for the Linear programming problems and a solver for Multiple Attribute Decision Making problems in combination with Parallel and Distributed Computing techniques based on a GRID configuration.

关键词： Multi-Objective programming Large Scale Problems Multiple Attribute Decision Making Parallel and Distributed Computing GRID Nets

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Data-driven Control of Polynomial Systems Using Dissipativity-Based inequalities and Petersen's Lemma 12

Data-driven Control of Polynomial Systems Using Dissipativit...

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12th international conference on Control Mechatronics and Automation

作者： Silva, Joao Gabriel N. Madeira, Diego de S. Correia, Wilkley B. Univ Fed Ceara Dept Elect Engn Fortaleza Ceara Brazil

ISBN: (纸本)9798331517519;9798331517526

In engineering science, the strategies of data-based control synthesis are valuable tools that allow to obtain a control law without the need to identify or to model the system through its related physics. However, the inherent presence of noise when acquiring data represents an obstacle in the validity of these data to represent accurately the system. In this paper, Lyapunov stability theory, dissipativity theory and Petersen's lemma are utilized to develop an algorithm. The proposed algorithm uses sum-of-squares programming to design a control law that guarantees asymptotic stability of polynomial systems with noisy data. In addition, the develop method is tested in comparison to a D-K iteration method in order to evaluate its performance in terms of computational costs.

关键词： dissipativity theory sum-of-squares programming data-driven nonlinear control

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Robust stability and control of nonlinear reheat power systems

Robust stability and control of nonlinear reheat power syste...

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2004 IEEE international conference on Control Applications

作者： Ismail, Abdulla Mahmoud, Magdi S. College of Engineering UAE University P. O. Pox 17555 Al-Ain United Arab Emirates

In this paper, the dynamic behavior of reheat power systems is represented by a class of nonlinear time-delay models. Both robust stability and state feedback control problems are considered. A convex programming approach is developed to establish tractable conditions expressed by linear matrix inequalities. The effect of finite feedback gains is cast into the analysis. Simulation results of a typical reheat power system are provided to illustrate the theoretical developments. © 2004 IEEE.

关键词： Electric power systems

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Checking existence of tolerance solutions of interval linear equations via mixed integer progrmming

Checking existence of tolerance solutions of interval linear...

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3rd international conference on Manufacturing Science and Engineering (ICMSE 2012)

作者： Wang, Huping Li, Wei Wang, Qin Zhao, Zhili Hangzhou Dianzi Univ Inst Operat Res & Cybernet Hangzhou 310018 Zhejiang Peoples R China China Jiliang Univ Coll Sci Hangzhou 310018 Peoples R China

ISBN: (纸本)9783037853726

An approach to deal with interval linear equations is to reduce the problem into solving several linear (or nonlinear) equations (or inequalities). To obtain characterations of the equations the paper gives a necessary condition of tolerance solutions of interval linear equations by means of nonlinear inequalities. Based on the necessary condition, a sufficience condition for nonexistence of tolerance solutions of the equations is given by use of the well-known Farkas theorem.

关键词： Interval linear equations 0-1 mixed integer programming tolerance solutions Farkas theorem

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Algorithms for Solving variational inequalities and Saddle Point Problems with Some Generalizations of Lipschitz Property for Operators 1

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20th international conference on Mathematical Optimization Theory and Operations Research , MOTOR 2021

作者： Titov, Alexander A. Stonyakin, Fedor S. Alkousa, Mohammad S. Gasnikov, Alexander V. Moscow Institute of Physics and Technology Moscow Russia V. I. Vernadsky Crimean Federal University Simferopol Russia HSE University Moscow Russia Institute for Information Transmission Problems RAS Moscow Russia Caucasus Mathematical Center Adyghe State University Maikop Russia

ISBN: (数字)9783030864330

ISBN: (纸本)9783030864323

The article is devoted to the development of numerical methods for solving saddle point problems and variational inequalities with simplified requirements for the smoothness conditions of functionals. Recently, some notable methods for optimization problems with strongly monotone operators were proposed. Our focus here is on newly proposed techniques for solving strongly convex-concave saddle point problems. One of the goals of the article is to improve the obtained estimates of the complexity of introduced algorithms by using accelerated methods for solving auxiliary problems. The second focus of the article is introducing an analogue of the boundedness condition for the operator in the case of arbitrary (not necessarily Euclidean) prox structure. We propose an analogue of the Mirror Descent method for solving variational inequalities with such operators, which is optimal in the considered class of problems. © 2021, Springer Nature Switzerland AG.

关键词： Numerical methods

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Robust H∞ filtering for polynomial nonlinear systems using sum of squares optimization

Robust H∞ filtering for polynomial nonlinear systems using ...

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2010 8th IEEE international conference on Control and Automation, ICCA 2010

作者： Zhao, Dan Wang, JianLiang School of Electrical and Electronic Engineering Nanyang Technological University Singapore 639798 Singapore

ISBN: (纸本)9781424451951

The robust H∞ filtering problem for the polynomial nonlinear systems against parametric uncertainty is investigated in this paper. By introducing additional matrix variables, we succeed in eliminating the coupling terms among system dynamics, filter dynamics and the Lyapunov matrix. Sufficient conditions to guarantee the filter stability with guaranteed H ∞ norm from the unknown norm-bounded disturbance signal to the estimation error are derived in terms of state dependent matrix inequalities, which provide an effective way for the application of the new sum of squares programming technique to obtain computationally tractable solutions. Robust H∞ filter is designed in an efficient computational manner. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed methodology. © 2010 IEEE.

关键词： nonlinear systems

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