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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.

Estratégias para resolução do problema MPEC. /

Yano, Flavio Sakakisbara. January 2003 (has links)
Orientador: Roberto Andreani / Banca: Ernesto Julián Goldberg Birgin / Banca: Geraldo Nunes Silva / Resumo: Problemas de programação matemática com restriçõesde equilíbrio (MPEC) são problemas de programação não-linear onde as restrições tem uma estrutura análoga condições necessárias de primeira ordem de um problema de otimização com restrições. Em formulações usuais do MPEC todos os pontos factíveis são não-regulares no sentido que não satisfazem a constraint qualification de Mangassarian-Fromovitz. Portanto, todos os pontos factíveis satisfazem a clássica condição necessária de fritz-john. Em princípio, isto poderia causar sérias dificuldades ao aplicarmos algoritmos de programação não-linear ao MPEC. Entretanto, muitos pontos factíveis do MPEC não satisfazem uma condição de otimalidade mais forte que Fritz-John, denominada condição AGP. Esta é a razão na qual em geral os algoritmos de programação não linear são satisfatórios quando aplicados ao MPEC. Nosso objetivo neste trabalho é discutir a aplicabilidade dos algoritmos de programação não-linear ao MPEC. / Mestre

Estratégias para resolução do problema MPEC

Yano, Flavio Sakakisbara [UNESP] 21 February 2003 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:27:08Z (GMT). No. of bitstreams: 0 Previous issue date: 2003-02-21Bitstream added on 2014-06-13T20:08:19Z : No. of bitstreams: 1 yano_fs_me_sjrp.pdf: 492262 bytes, checksum: d370b857c12f73d6431598e15dc347ff (MD5) / Problemas de programação matemática com restriçõesde equilíbrio (MPEC) são problemas de programação não-linear onde as restrições tem uma estrutura análoga condições necessárias de primeira ordem de um problema de otimização com restrições. Em formulações usuais do MPEC todos os pontos factíveis são não-regulares no sentido que não satisfazem a constraint qualification de Mangassarian-Fromovitz. Portanto, todos os pontos factíveis satisfazem a clássica condição necessária de fritz-john. Em princípio, isto poderia causar sérias dificuldades ao aplicarmos algoritmos de programação não-linear ao MPEC. Entretanto, muitos pontos factíveis do MPEC não satisfazem uma condição de otimalidade mais forte que Fritz-John, denominada condição AGP. Esta é a razão na qual em geral os algoritmos de programação não linear são satisfatórios quando aplicados ao MPEC. Nosso objetivo neste trabalho é discutir a aplicabilidade dos algoritmos de programação não-linear ao MPEC.

Enhanced Optimality Conditions and New Constraint Qualifications for Nonsmooth Optimization Problems

Zhang, Jin 12 December 2014 (has links)
The main purpose of this dissertation is to investigate necessary optimality conditions for a class of very general nonsmooth optimization problems called the mathematical program with geometric constraints (MPGC). The geometric constraint means that the image of certain mapping is included in a nonempty and closed set. We first study the conventional nonlinear program with equality, inequality and abstract set constraints as a special case of MPGC. We derive the enhanced Fritz John condition and from which, we obtain the enhanced Karush-Kuhn-Tucker (KKT) condition and introduce the associated pseudonormality and quasinormality condition. We prove that either pseudonormality or quasinormality with regularity implies the existence of a local error bound. We also give a tighter upper estimate for the Fr\'chet subdifferential and the limiting subdifferential of the value function in terms of quasinormal multipliers which is usually a smaller set than the set of classical normal multipliers. We then consider a more general MPGC where the image of the mapping from a Banach space is included in a nonempty and closed subset of a finite dimensional space. We obtain the enhanced Fritz John necessary optimality conditions in terms of the approximate subdifferential. One of the technical difficulties in obtaining such a result in an infinite dimensional space is that no compactness result can be used to show the existence of local minimizers of a perturbed problem. We employ the celebrated Ekeland's variational principle to obtain the results instead. We then apply our results to the study of exact penalty and sensitivity analysis. We also study a special class of MPCG named mathematical programs with equilibrium constraints (MPECs). We argue that the MPEC-linear independence constraint qualification is not a constraint qualification for the strong (S-) stationary condition when the objective function is nonsmooth. We derive the enhanced Fritz John Mordukhovich (M-) stationary condition for MPECs. From this enhanced Fritz John M-stationary condition we introduce the associated MPEC generalized pseudonormality and quasinormality condition and build the relations between them and some other widely used MPEC constraint qualifications. We give upper estimates for the subdifferential of the value function in terms of the enhanced M- and C-multipliers respectively. Besides, we focus on some new constraint qualifications introduced for nonlinear extremum problems in the recent literature. We show that, if the constraint functions are continuously differentiable, the relaxed Mangasarian-Fromovitz constraint qualification (or, equivalently, the constant rank of the subspace component condition) implies the existence of local error bounds. We further extend the new result to the MPECs. / Graduate / 0405

Distributed Computational Methods for Energy Management in Smart Grids

Mohammadi, Javad 01 September 2016 (has links)
It is expected that the grid of the future differs from the current system by the increased integration of distributed generation, distributed storage, demand response, power electronics, and communications and sensing technologies. The consequence is that the physical structure of the system becomes significantly more distributed. The existing centralized control structure is not suitable any more to operate such a highly distributed system. This thesis is dedicated to providing a promising solution to a class of energy management problems in power systems with a high penetration of distributed resources. This class includes optimal dispatch problems such as optimal power flow, security constrained optimal dispatch, optimal power flow control and coordinated plug-in electric vehicles charging. Our fully distributed algorithm not only handles the computational complexity of the problem, but also provides a more practical solution for these problems in the emerging smart grid environment. This distributed framework is based on iteratively solving in a distributed fashion the first order optimality conditions associated with the optimization formulations. A multi-agent viewpoint of the power system is adopted, in which at each iteration, every network agent updates a few local variables through simple computations, and exchanges information with neighboring agents. Our proposed distributed solution is based on the consensus+innovations framework, in which the consensus term enforces agreement among agents while the innovations updates ensure that local constraints are satisfied.

Study on Optimality Conditions in Stochastic Linear Programming

Zhao, Lei January 2005 (has links)
In the rapidly changing world of today, people have to make decisions under some degree of uncertainty. At the same time, the development of computing technologies enables people to take uncertain factors into considerations while making their decisions.Stochastic programming techniques have been widely applied in finance engineering, supply chain management, logistics, transportation, etc. Such applications often involve a large, possibly infinite, set of scenarios. Hence the resulting programstend to be large in scale.The need to solve large scale programs calls for a combination of mathematical programming techniques and sample-based approximation. When using sample-based approximations, it is important to determine the extent to which the resulting solutions are dependent on thespecific sample used. This dissertation research focuses on computational evaluation of the solutions from sample-based two-stage/multistage stochastic linear programming algorithms, with a focus on the effectiveness of optimality tests and the quality ofa proposed solution.In the first part of this dissertation, two alternative approaches of optimality tests of sample-based solutions, adaptive and non-adaptive sampling methods, are examined and computationally compared. The results of the computational experiment are in favor of the adaptive methods. In the second part of this dissertation, statistically motivated bound-based solution validation techniques in multistage linear stochastic programs are studied both theoretically and computationally. Different approaches of representations of the nonanticipativity constraints are studied. Bounds are established through manipulations of the nonanticipativity constraints.

Condições suficientes de otimalidade para o problema de controle de sistemas lineares estocásticos / Sufficient optimality conditions for the control problem of linear stochastic systems

Madeira, Diego de Sousa 20 August 2018 (has links)
Orientador: João Bosco Ribeiro do Val / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-20T16:10:11Z (GMT). No. of bitstreams: 1 Madeira_DiegodeSousa_M.pdf: 382775 bytes, checksum: d75575b4a57a5bb98739210edef9b5c7 (MD5) Previous issue date: 2012 / Resumo: As principais contribuições deste trabalho são a obtenção de condições necessárias e suficientes de otimalidade para o problema de controle de sistemas lineares determinísticos discretos e para certas classes de sistemas lineares estocásticos. Adotamos o método de controle por realimentação de saída, um horizonte de controle finito e um funcional de custo quadrático nas variáveis de estado e de controle. O problema determinístico é solucionado por completo, ou seja, provamos que para qualquer sistema MIMO as condições necessárias de otimalidade são também suficientes. Para tanto, uma versão do Princípio do Máximo Discreto é utilizada. Além disso, analisamos o caso estocástico com ruído aditivo e provamos que o princípio do máximo discreto fornece as condições necessárias de otimalidade para o problema, embora não garanta suficiência. Por fim, em um cenário particular com apenas dois estágios, empregamos uma técnica de parametrização do funcional de custo associado ao sistema linear estocástico com ruído aditivo e provamos que, no caso dos sistemas SISO com matrizes C (saída) e B (entrada) tais que CB = 0, as condições necessárias de otimalidade são também suficientes. Provamos que o mesmo também é válido para a classe dos Sistemas Lineares com Saltos Markovianos (SLSM), no contexto especificado. Com o objetivo de ilustrar numericamente os resultados teóricos obtidos, alguns exemplos numéricos são fornecidos / Abstract: The main contributions of this work are that the necessary and sufficient optimality conditions for the control problem of discrete linear deterministic systems and some classes of linear stochastic systems are obtained. We adopted the output feedback control method, a finite horizon control and a cost function that is quadratic in the state and control vectors. The deterministic problem is completely solved, that is, we prove that for any MIMO system the necessary optimality conditions are also sufficient. To do so, a formulation of the Discrete Maximum Principle is used. Furthermore, we analyze the stochastic case with additive noise and prove that the discrete maximum principle provides the necessary optimality conditions, though they are not sufficient. Finally, in a particular two-stage scenario, we apply a parametrization technique of the cost function associated with the linear stochastic system with additive noise and prove that, for SISO systems with orthogonal matrices C (output) and B (input) so that CB = 0, the necessary optimality conditions are sufficient too. We prove that under the underlined context the previous statement is also valid in the case of the Markov Jump Linear Systems (MJLS). In order to illustrate the theoretical results obtained, some numerical examples are given / Mestrado / Automação / Mestre em Engenharia Elétrica

Condições sequenciais de otimalidade / Sequential optimality conditions

Haeser, Gabriel 09 April 2009 (has links)
Orientador: Jose Mario Martinez / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-14T02:27:22Z (GMT). No. of bitstreams: 1 Haeser_Gabriel_D.pdf: 1980596 bytes, checksum: 34e962c907bf0b544d52deba5e4555e6 (MD5) Previous issue date: 2009 / Resumo: Estudamos as condições de otimalidade provenientes dos algoritmos de penalidade externa, penalidade interna, penalidade interna-externa e restauração inexata, e mostramos relações com a CPLD, uma nova condição de qualificação estritamente mais fraca que a condição de Mangasarian-Fromovitz e a condição de posto constante de Janin. Estendemos o resultado do clássico Lema de Carathéodory, onde mostramos um limitante para o tamanho dos novos multiplicadores. Apresentamos novas condições de otimalidade relacionadas à condição AGP (Approximate Gradient Projection). Quando há um conjunto extra de restrições lineares, definimos uma condição do tipo AGP e provamos relações com a CPLD e as equações KKT. Resultados similares são obtidos quando há um conjunto extra de restrições convexas. Mostramos também algumas generalizações e relações com um algoritmo de restauração inexata. / Abstract: We study optimality conditions generated by the external penalty, internal penalty, internal-external penalty and inexact restoration algorithms, and we show relations with the CPLD, a new constraint qualification strictly weaker than the Mangasarian-Fromovitz condition and the constant rank condition of Janin. We extend the result of the classical Carathéodory's Lemma, where we show a bound for the size of the new multipliers. We present new optimality conditions related to the Approximate Gradient Projection condition (AGP). When there is an extra set of linear constraints, we define an AGP type condition and prove relations with CPLD and KKT conditions. Similar results are obtained when there is an extra set of convex constraints. We provide some further generalizations and relations to an inexact restoration algorithm. / Doutorado / Otimização / Doutor em Matemática Aplicada

Análise não suave e aplicações em otimização

Costa, Tiago Mendonça de [UNESP] 28 February 2011 (has links) (PDF)
Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-28Bitstream added on 2014-06-13T20:48:40Z : No. of bitstreams: 1 costa_tm_me_sjrp.pdf: 1425800 bytes, checksum: f5b08954e14201ee5211145299b1e813 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, estamos interessados em apresentar uma abordagem relacionando a análise não suave com a otimização. Primeiramente, é realizado um estudo sobre conceitos da análise não suave, como cones normais, cone tangente de Bouligand, subdiferenciais proximal, estrita, limite e de clarke. Com esses conceitos exibimos uma série de resultados, por exemplo, uma caracterização par funções de Lipschitz, subdiferencais da soma, produto e máximo de funções semi-contínuas inferior, uma versão não suave dos multiplicadores de Lagrange, i.e., condições de primeira ordem para otimalidade de problemas de otimização não suaves. Também é feito um estudo sobre as condições de segunda ordem para otimalidade em problemas de otimização não suaves e para isso, foi necessário a apresentação de outros conceitos e propriedades como os de Hessiana generalizada, Jacobiana aproximada a Hessiana proximada. Após a apresentação desses resultados, é feita uma análise sobre dois Teoremas que fornecem, com abordagens distintas, condições suficiente de segunda ordem para problemas de otimização não suaves e este trabalho é finalizado com a aprsentação de um resultado que é considerado uma unificação desses dois Teoremas / In this work we are interested in the presentation of an approach relating Nonsmooth Analysis to Optimization. First we make a study about concepts of nonsmooth analysis such as, normal cone, Bouligand's tangent cone, proximal, strict and limiting Subdiferential, as well as Clarke's Suddifferential. After these, we exhibit a series of results, for example, a characterization of Lipschitz functions, Subdifferential sum, product and maxium rules of lower semicontinuous functions and a nonsmooth version of Lagrange's multiplier rule, that is, a first order necessary condition of optimality for nonsmooth optimization problems. We also made a study about second order optimality conditions for nonsmooth optimization problems. In order to do that, it was necessary to present other concepts and properties about generalized Hessian, approximate Jacobian and approximate Hessian. After presenting these concepts and results, an analysis of two theorems that provide, with different approches, second order conditions for optimality for nonsmooth problems is made. Finally, this dissertation is completed with the exposition of a result that is considered a unification of these two theorems

Second Order Sufficient Optimality Conditions for Nonlinear Parabolic Control Problems with State Constraints

Raymond, Jean-Pierre, Tröltzsch, Fredi 30 October 1998 (has links) (PDF)
In this paper, optimal control problems for semilinear parabolic equations with distributed and boundary controls are considered. Pointwise constraints on the control and on the state are given. Main emphasis is laid on the discussion of second order sufficient optimality conditions. Sufficiency for local optimality is verified under different assumptions imposed on the dimension of the domain and on the smoothness of the given data.

Sur les dérivées généralisées, les conditions d'optimalité et l'unicité des solutions en optimisation non lisse / On generalized derivatives, optimality conditions and uniqueness of solutions in nonsmooth optimization

Le Thanh, Tung 13 August 2011 (has links)
En optimisation les conditions d’optimalité jouent un rôle primordial pour détecter les solutions optimales et leur étude occupe une place significative dans la recherche actuelle. Afin d’exprimer adéquatement des conditions d’optimalité les chercheurs ont introduit diverses notions de dérivées généralisées non seulement pour des fonctions non lisses, mais aussi pour des fonctions à valeurs ensemblistes, dites applications multivoques ou multifonctions. Cette thèse porte sur l’application des deux nouveaux concepts de dérivées généralisées: les ensembles variationnels de Khanh-Tuan et les approximations de Jourani-Thibault, aux problèmes d’optimisation multiobjectif et aux problèmes d’équilibre vectoriel. L’enjeu principal est d’obtenir des conditions d’optimalité du premier et du second ordre pour les problèmes ayant des données multivoques ou univoques non lisses et pas forcément continues, et des conditions assurant l’unicité des solutions dans les problèmes d’équilibre vectoriel. / Optimality conditions for nonsmooth optimization have become one of the most important topics in the study of optimization-related problems. Various notions of generalized derivatives have been introduced to establish optimality conditions. Besides establishing optimality conditions, generalized derivatives also is an important tool for studying the local uniqueness of solutions. During the last three decades, these topics have been being developed, generalized and applied to many elds of mathematics by many authors all over the world. The purpose of this thesis is to investigate the above topics. It consists of ve chapters. In Chapter 1, we develop elements of calculus of variational sets for set-valued mappings, which were recently introduced in Khanh and Tuan (2008). Most of the usual calculus rules, from chain and sum rules to rules for unions, intersections, products and other operations on mappings, are established. As applications we provide a direct employment of sum rules to establishing an explicit formula for a variational set of the solution map to a parametrized variational inequality in terms of variational sets of the data. Furthermore, chain rules and sum or product rules are also used to prove optimality conditions for weak solutions of some vector optimization problems. In Chapter 2, we propose notions of higher-order outer and inner radial derivatives of set-valued maps and obtain main calculus rules. Some direct applications of these rules in proving optimality conditions for particular optimization problems are provided. Then, we establish higher-order optimality necessary conditions and sufficient ones for a general set-valued vector optimization problem with inequality constraints. Chapter 3 is devoted to using first and second-order approximations, which were introduced by Jourani and Thibault (1993) and Allali and Amaroq (1997), as generalized derivatives, to establish both necessary and sufficient optimality conditions for various kinds of solutions to nonsmooth vector equilibrium problems with functional constraints. Our rst-order conditions are shown to be applicable in many cases, where existing ones cannot be applied. The second-order conditions are new. In Chapter 4, we consider nonsmooth multi-objective fractional programming on normed spaces. Using rst and second-order approximations as generalized derivatives, rst and second-order optimality conditions are established. For sufficient conditions no convexity is needed. Our results can be applied even in innite dimensional cases involving innitely discontinuousmaps. In Chapter 5, we establish sufficient conditions for the local uniqueness of solutions to nonsmooth strong and weak vector equilibrium problems. Also by using approximations, our results are valid even in cases where the maps involved in the problems suffer innite discontinuity at the considered point.

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