Download or read book Decomposition of Variational Inequalities with Applications to Nash Cournot Models in Time of Use Electricity Markets written by Emre Celebi and published by . This book was released on 2011 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis proposes equilibrium models to link the wholesale and retail electricity markets which allow for reconciliation of the differing time scales of responses of producers (e.g., hourly) and consumers (e.g., monthly) to changing prices. Electricity market equilibrium models with time of use (TOU) pricing scheme are formulated as large-scale variational inequality (VI) problems, a unified and concise approach for modeling the equilibrium. The demand response is dynamic in these models through a dependence on the lagged demand. Different market structures are examined within this context. With an illustrative example, the welfare gains/losses are analyzed after an implementation of TOU pricing scheme over the single pricing scheme. An approximation of the welfare change for this analysis is also presented. Moreover, break-up of a large supplier into smaller parts is investigated. For the illustrative examples presented in the dissertation, overall welfare gains for consumers and lower prices closer to the levels of perfect competition can be realized when the retail pricing scheme is changed from single pricing to TOU pricing. These models can be useful policy tools for regulatory bodies i) to forecast future retail prices (TOU or single prices), ii) to examine the market power exerted by suppliers and iii) to measure welfare gains/losses with different retail pricing schemes (e.g., single versus TOU pricing). With the inclusion of linearized DC network constraints into these models, the problem size grows considerably. Dantzig-Wolfe (DW) decomposition algorithm for VI problems is used to alleviate the computational burden and it also facilitates model management and maintenance. Modification of the DW decomposition algorithm and approximation of the DW master problem significantly improve the computational effort required to find the equilibrium. These algorithms are applied to a two-region energy model for Canada and a realistic Ontario electricity test system. In addition to empirical analysis, theoretical results for the convergence properties of the master problem approximation are presented for DW decomposition of VI problems.

Download or read book Complementarity Modeling in Energy Markets written by Steven A. Gabriel and published by Springer Science & Business Media. This book was released on 2012-07-20 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: This addition to the ISOR series introduces complementarity models in a straightforward and approachable manner and uses them to carry out an in-depth analysis of energy markets, including formulation issues and solution techniques. In a nutshell, complementarity models generalize: a. optimization problems via their Karush-Kuhn-Tucker conditions b. on-cooperative games in which each player may be solving a separate but related optimization problem with potentially overall system constraints (e.g., market-clearing conditions) c. conomic and engineering problems that aren’t specifically derived from optimization problems (e.g., spatial price equilibria) d. roblems in which both primal and dual variables (prices) appear in the original formulation (e.g., The National Energy Modeling System (NEMS) or its precursor, PIES). As such, complementarity models are a very general and flexible modeling format. A natural question is why concentrate on energy markets for this complementarity approach? s it turns out, energy or other markets that have game theoretic aspects are best modeled by complementarity problems. The reason is that the traditional perfect competition approach no longer applies due to deregulation and restructuring of these markets and thus the corresponding optimization problems may no longer hold. Also, in some instances it is important in the original model formulation to involve both primal variables (e.g., production) as well as dual variables (e.g., market prices) for public and private sector energy planning. Traditional optimization problems can not directly handle this mixing of primal and dual variables but complementarity models can and this makes them all that more effective for decision-makers.

Download or read book Nash Equilibrium Problems in Power Markets and Product Design Analysis and Algorithms written by Aswin Kannan and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this research is on the analysis and computation of equilibria in noncooperative Cournot and Bertrand games. The application of focus for Cournot competition is power markets while that for Bertrand competition is product design. We consider Cournot-based models for strategic behavior in power markets while Bertrandbased models are employed for analyzing the behavior of price-based competition in product design. This thesis is partitioned into three parts. Of these, the rst two parts focus on power market applications while the third part focuses on product design. Motivated by the risk of capacity shortfall faced by market participants with uncertain generation assets, the rst part considers a game where agents are assumed to be risk-averse optimizers, using a conditional value-at-risk (CVaR) measure. The resulting game-theoretic problem is a two-period risk-based stochastic Nash game with shared strategy sets. In general, this stochastic game has nonsmooth objectives and standard existence and uniqueness results cannot be leveraged for this class of games, given the lack of compactness of strategy sets and the absence of strong monotonicity in the gradient map of the objectives. However, when the risk-measure is independent of competitive interactions, a subset of equilibria to the risk-averse game are shown to be characterized by a solvable monotone single-valued variational inequality. If the risk-measures are generalized to allow for strategic interactions, then the characterization is through a multi-valued variational inequality. Both this object and its single-valued counterpart, arising from the smoothed game, are shown to admit solutions. The equilibrium conditions of the game grow linearly in size with the the sample-space, network size and the number of participating rms. Consequently, direct schemes are inadvisable for most practical problems and instead, we present a distributed regularized primaldual and dual projection scheme where both primal and dual iterates are computed separately. Rate of convergence estimates are provided and error bounds are developed for inexact extensions of the dual scheme. Unlike projection schemes for deterministic problems, here the projection step requires the solution of a possibly massive stochastic program. By utilizing cutting plane methods, we ensure that the complexity of the projection scheme scales slowly with the size of the sample-space. Insights regarding market design and operation are obtained after testing the model on a 53-node electricity network. The second part extends this model by considering the grid operator to be a pro t maximizer. However the effect of risk is neglected in this model. The resulting problem is a quasi variational inequality. An analysis of the equivalent complementarity problem (CP) allows us to claim that the game does admit an equilibrium. By observing that the CP is monotone, we are in a position to employ a class of iterative regularization techniques namely the iterative Tikhonov and the iterative proximal algorithms. The algorithms are seen to scale well with the size of the problem. The model is employed for examining strategic behavior on a twelve node network and several economic insights are drawn. The third part of this thesis deals with Bertrand competition in a product design regime. With due consideration to the attribute dimension in addition to price competition, more specifically for design and consumer service industries, a game theoretic model is formulated. The logit model, in lieu of some of its tractable properties, is deployed to capture consumer preferences and thereby the demand. Subsequently the variational formulations corresponding to the game are analyzed for existence of solutions. The lack of convexity of objectives, analytical intractability of the variational formulations corresponding to the game state some drawbacks of the logit model. Several projection and interior point schemes are deployed for solving these classes of problems. Numerical results for smaller instances of these games are illustrated by means of a painkiller example. Suggestions on alternate revenue maximization models are presented.

Download or read book INFORMS Annual Meeting written by Institute for Operations Research and the Management Sciences. National Meeting and published by . This book was released on 2006 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Analysis of Variational Inequalities written by R. Trémolières and published by Elsevier. This book was released on 2011-08-18 with total page 807 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Analysis of Variational Inequalities

Download or read book Convergence Analysis of Proximal like Methods for Variational Inequalities and Fixed Point Problems written by Nils Langenberg and published by Logos Verlag Berlin GmbH. This book was released on 2011 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: Several regularization methods for variational inequalities and fixed point problems are studied. Known convergence results especially require some kind of monotonicity of the problem data as well as, especially for Bregman-function-based algorithms, some additional assumption known as the cutting plane property. Unfortunately, these assumptions may be considered as rather restrictive e.g. in the framework of Nash equilibrium problems. This motivates the development of convergence results under weaker hypotheses which constitute the major subject of the present book. Studied methods include the Bregman-function-based Proximal Point Algorithm (BPPA), Cohen's Auxiliary Problem Principle and an extragradient algorithm.Moreover, this work also contains the first numerical comparison of stopping criteria in the framework of the BPPA. Although such conditions are the subject of theoretical investigations frequently, their numerical effectiveness and a deducible preference were still unknown. This gives rise to the necessity of the presented numerical experiments.

Download or read book Competition and Equilibria in Electricity Markets Based on Two settlement System written by David Watts and published by . This book was released on 2007 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Variational Inequalities and Network Equilibrium Problems written by F. Giannessi and published by Springer. This book was released on 2013-06-26 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.

Download or read book Variational and Hemivariational Inequalities Theory Methods and Applications written by D. Goeleven and published by Springer. This book was released on 2013-11-22 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.

Download or read book Variational and Hemivariational Inequalities Theory Methods and Applications written by DANIEL Goeleven and published by Springer. This book was released on 2013-12-01 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.

Download or read book Pure and Applied Mathematics written by and published by . This book was released on 1980 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Equilibrium Problems Nonsmooth Optimization and Variational Inequality Models written by F. Giannessi and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the book is to cover the three fundamental aspects of research in equilibrium problems: the statement problem and its formulation using mainly variational methods, its theoretical solution by means of classical and new variational tools, the calculus of solutions and applications in concrete cases. The book shows how many equilibrium problems follow a general law (the so-called user equilibrium condition). Such law allows us to express the problem in terms of variational inequalities. Variational inequalities provide a powerful methodology, by which existence and calculation of the solution can be obtained.

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2007 with total page 924 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partitionable Variational Inequalities and an Application to the Market Equilibrium Problem written by Steven Chandler McKelvey and published by . This book was released on 1989 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partitionable Variational Inequalities Nad an Application to the Market Equilibrium Problem written by Steven Chandler Mckelvey and published by . This book was released on 1991 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Inequality Problems in Mechanics and Applications written by Panagiotis D. Panagiotopoulos and published by . This book was released on 1985 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Programs with Equilibrium Constraints written by Zhi-Quan Luo and published by Cambridge University Press. This book was released on 1996-11-13 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive study for an important class of constrained optimisation problems known as Mathematical Programs with Equilibrium Constraints.