Thematische Bibliographien / Infinite-Dimensional linear programming

Auswahl der wissenschaftlichen Literatur zum Thema „Infinite-Dimensional linear programming“

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Veröffentlicht am 1. Juni 2024

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Zeitschriftenartikel zum Thema "Infinite-Dimensional linear programming"

Appa, Gautam, Edward J. Anderson und Peter Nash. „Linear Programming in Infinite-Dimensional Spaces“. Journal of the Operational Research Society 40, Nr. 1 (Januar 1989): 109. http://dx.doi.org/10.2307/2583085.

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Appa, Gautam. „Linear Programming in Infinite-Dimensional Spaces“. Journal of the Operational Research Society 40, Nr. 1 (Januar 1989): 109–10. http://dx.doi.org/10.1057/jors.1989.13.

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Romeijn, H. Edwin, Robert L. Smith und James C. Bean. „Duality in infinite dimensional linear programming“. Mathematical Programming 53, Nr. 1-3 (Januar 1992): 79–97. http://dx.doi.org/10.1007/bf01585695.

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López, M. A. „Linear programming in infinite-dimensional spaces“. European Journal of Operational Research 36, Nr. 1 (Juli 1988): 134–35. http://dx.doi.org/10.1016/0377-2217(88)90019-7.

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Romeijn, H. Edwin, und Robert L. Smith. „Shadow Prices in Infinite-Dimensional Linear Programming“. Mathematics of Operations Research 23, Nr. 1 (Februar 1998): 239–56. http://dx.doi.org/10.1287/moor.23.1.239.

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Ho, Tvu-Ying, Yuung-Yih Lur und Soon-Yi Wu. „The Difference between Finite Dimensional Linear Programming Problems and Infinite Dimensional Linear Programming Problems“. Journal of Mathematical Analysis and Applications 207, Nr. 1 (März 1997): 192–205. http://dx.doi.org/10.1006/jmaa.1997.5279.

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Taksar, Michael I. „Infinite-Dimensional Linear Programming Approach to SingularStochastic Control“. SIAM Journal on Control and Optimization 35, Nr. 2 (März 1997): 604–25. http://dx.doi.org/10.1137/s036301299528685x.

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Vinh, N. T., D. S. Kim, N. N. Tam und N. D. Yen. „Duality gap function in infinite dimensional linear programming“. Journal of Mathematical Analysis and Applications 437, Nr. 1 (Mai 2016): 1–15. http://dx.doi.org/10.1016/j.jmaa.2015.12.043.

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Balbas, Alejandro, und Antonio Heras. „Duality theory for infinite-dimensional multiobjective linear programming“. European Journal of Operational Research 68, Nr. 3 (August 1993): 379–88. http://dx.doi.org/10.1016/0377-2217(93)90194-r.

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Kariotoglou, Nikolaos, Maryam Kamgarpour, Tyler H. Summers und John Lygeros. „The Linear Programming Approach to Reach-Avoid Problems for Markov Decision Processes“. Journal of Artificial Intelligence Research 60 (04.10.2017): 263–85. http://dx.doi.org/10.1613/jair.5500.

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One of the most fundamental problems in Markov decision processes is analysis and control synthesis for safety and reachability specifications. We consider the stochastic reach-avoid problem, in which the objective is to synthesize a control policy to maximize the probability of reaching a target set at a given time, while staying in a safe set at all prior times. We characterize the solution to this problem through an infinite dimensional linear program. We then develop a tractable approximation to the infinite dimensional linear program through finite dimensional approximations of the decision space and constraints. For a large class of Markov decision processes modeled by Gaussian mixtures kernels we show that through a proper selection of the finite dimensional space, one can further reduce the computational complexity of the resulting linear program. We validate the proposed method and analyze its potential with numerical case studies.

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Dissertationen zum Thema "Infinite-Dimensional linear programming"

Badikov, Sergey. „Infinite-dimensional linear programming and model-independent hedging of contingent claims“. Thesis, Imperial College London, 2017. http://hdl.handle.net/10044/1/59069.

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We consider model-independent pathwise hedging of contingent claims in discrete-time markets, in the framework of infinite-dimensional linear programmes (LP). The dual problem can be formulated as optimization over the set of martingale measures subject to market constraints. Absence of model-independent arbitrage plays a crucial role in ensuring that both the primal and the dual problems are well posed and there is no duality gap. In fact we show that different notions of model-independent arbitrage are required to prove duality results in various settings. We then specialize this duality theory to the situation where European Call options are traded on the market. In particular we consider hedging portfolios that consist of static positions in traded options and a dynamic trading strategy. The dual variables are then constrained to martingale measures consistent with prices of traded options. When only finitely many Call options are traded, the notion of weak arbitrage introduced in Davis and Hobson (2007) is sufficient to ensure absence of duality gap between the primal and the dual problems. In this case the set of feasible dual variables is not closed, and extrapolation of Call option prices (equivalently of the implied volatility smile) is required. We finally provide numerical examples to support our theoretical claims. By discretizing the infinite-dimensional LPs, we compute arbitrage-free price bounds for Forward-Start options. We further perform a sensitivity analysis of the aforementioned extrapolation and find that in the case of Forward- Start options it does not significantly influence arbitrage bounds obtained by numerically solving discretized problems.

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Leutscher, de las Nieves Marcos. „Contributions to the linear programming approach for mean field games and its applications to electricity markets“. Electronic Thesis or Diss., Institut polytechnique de Paris, 2022. http://www.theses.fr/2022IPPAG010.

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Cette thèse présente trois contributions principales liées à l'approche de programmation linéaire pour les jeux à champ moyen (MFGs).La première partie de la thèse traite les aspects théoriques des MFGs permettant simultanément arrêt optimal, contrôle stochastique et absorption. En utilisant la formulation de programmation linéaire pour ce type de MFGs, un résultat général d'existence pour les équilibres de Nash MFG est dérivé sous des hypothèses faibles à travers du théorème de point fixe de Kakutani-Fan-Glicksberg. Nous montrons que cette méthode de relaxation est équivalente à l'approche par martingales contrôlées/arrêtées pour les MFG, une autre méthode de relaxation utilisée dans des articles précédents dans le cas du contrôle. De plus, sous des conditions appropriées, nous montrons que notre notion de solution satisfait un système d'équations différentielles partielles (EDP), ce qui permet de comparer nos résultats avec la littérature sur les EDP.La deuxième partie se concentre sur un algorithme numérique pour l'approximation de l'équilibre de Nash MFG en tirant profit de l'approche par programmation linéaire. La convergence de cet algorithme est démontrée pour deux classes de MFG, les MFG avec arrêt optimal et absorption, et les MFG avec contrôle stochastique et absorption. Le schéma numérique appartient à la classe des procédures d'apprentissage. En particulier, nous appliquons l'algorithme Fictitious Play où la meilleure réponse à chaque itération est calculée en résolvant un problème de programmation linéaire.La dernière partie de la thèse porte sur une application des MFGs à la dynamique long terme de l'industrie de l'électricité. Différents scénarios macroéconomiques et de politique climatique sont possibles pour les années à venir, or le scénario exact reste incertain. Par conséquent, les producteurs conventionnels ou renouvelables visant à sortir du marché ou à y entrer, respectivement, sont confrontés à l'incertitude concernant le prix du carbone et les politiques climatiques à venir. Les deux classes de producteurs interagissent par le biais du prix de l'électricité. Des stratégies d'équilibre de Nash sur des temps d'arrêt sont considérées et le problème est analysé à travers d'un modèle MFG. À cette fin, nous développons l'approche de programmation linéaire pour les MFG d'arrêt optimal avec bruit commun et information partielle en temps discret. Nous montrons l'existence d'un équilibre de Nash MFG et l'unicité du prix de marché en équilibre. Enfin, nous étendons l'algorithme numérique développé dans la deuxième partie de la thèse pour illustrer le modèle avec un exemple empirique inspiré du marché de l'électricité britannique
This thesis presents three main contributions related to the linear programming approach for mean field games (MFGs).The first part of the thesis is concerned with the theoretical aspects of MFGs allowing simultaneously for optimal stopping, stochastic control and absorption. Using the linear programming formulation for this type of MFGs, a general existence result for MFG Nash equilibria is derived under mild assumptions by means of Kakutani-Fan-Glicksberg's fixed point theorem. This relaxation method is shown to be equivalent to the controlled/stopped martingale approach for MFGs, another relaxation method used in earlier papers in the pure control case. Furthermore, under appropriate conditions, we show that our notion of solution satisfies a partial differential equation (PDE) system, allowing to compare our results with the PDE literature.The second part focuses on a numerical algorithm for approximating the MFG Nash equilibrium taking advantage of the linear programming approach. The convergence of this algorithm is shown for two classes of MFG, MFGs with optimal stopping and absorption, and MFGs with stochastic control and absorption. The numerical scheme belongs to the class of learning procedures. In particular, we apply the Fictitious Play algorithm where the best response at each iteration is computed by solving a linear programming problem.The last part of the thesis deals with an application of MFGs to the long term dynamics of the electricity industry. Different macroeconomic and climate policy scenarios are possible for the coming years, and the exact scenario remains uncertain. Therefore, conventional or renewable producers aiming to exit or enter the market, respectively, are facing uncertainty about the future carbon price and climate policies. Both classes of producers interact through the electricity market price. Nash equilibrium strategies over stopping times are considered and the problem is analyzed through a MFG model. To this end, we develop the linear programming approach for MFGs of optimal stopping with common noise and partial information in discrete time. We show the existence of an MFG Nash equilibrium and the uniqueness of the equilibrium market price. Finally, we extend the numerical algorithm developed in the second part of the thesis to illustrate the model with an empirical example inspired by the UK electricity market

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Bo-JyunJian und 簡伯均. „An algorithm for infinite-dimensional linear programming problems on Lp space“. Thesis, 2010. http://ndltd.ncl.edu.tw/handle/35605374250240399546.

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碩士
國立成功大學
數學系應用數學碩博士班
98
This thesis studies the infinite-dimensional linear programming problems of integral type. The decision variable is taken in the Lp space where 1＜p＜infty and required to have an upper bound and a lower bound by continuous functions on a compact interval. To simplify the original problems, we transform them to equivalent problems. Two numerical algorithms are proposed for solving these problems and the convergence properties of the algorithms are given. Some numerical examples are also given to implement the proposed algorithms.

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Bücher zum Thema "Infinite-Dimensional linear programming"

Anderson, E. J. Linear programming in infinite-dimensional spaces: Theory and applications. Chichester [West Sussex]: Wiley, 1987.

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1954-, Anderson E. J., und Philpott A. B. 1956-, Hrsg. Infinite programming: Proceedings of an International Symposium on Infinite Dimensional Linear Programming, held at Churchill College, Cambridge, United Kingdom, September 7-10, 1984. Berlin: Springer-Verlag, 1985.

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Banks, H. Thomas. Optimal feedback control infinite dimensional parabolic evolution systems: Approximation techniques. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1989.

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N, Iusem Alfredo, Hrsg. Totally convex functions for fixed points computation and infinite dimensional optimization. Dordrecht: Kluwer Academic Publishers, 2000.

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Philpott, Andrew B., und Edward J. Anderson. Infinite Programming: Proceedings of an International Symposium on Infinite Dimensional Linear Programming Churchill College, Cambridge, United Kingdom, September 7-10 1984. Springer London, Limited, 2012.

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Butnariu, D., und A. N. Iusem. Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization. Springer, 2012.

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Butnariu, D., und A. N. Iusem. Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization (Applied Optimization). Springer, 2000.

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Buchteile zum Thema "Infinite-Dimensional linear programming"

Rubio, J. E. „Nonlinear Optimal Control Problems as Infinite-Dimensional Linear Programming Problems“. In Lecture Notes in Economics and Mathematical Systems, 172–84. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-46564-2_13.

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„On the Approximation of an Infinite-Dimensional Linear Programming Problem“. In Proceedings of the Eighth International Colloquium on Differential Equations, Plovdiv, Bulgaria, 18–23 August, 1997, 153–60. De Gruyter, 1998. http://dx.doi.org/10.1515/9783112313923-023.

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Konferenzberichte zum Thema "Infinite-Dimensional linear programming"

Elia, Nicola, Munther A. Dahleh und Ignacio J. Diaz-Bobillo. „Controller Design via Infinite-Dimensional Linear Programming“. In 1993 American Control Conference. IEEE, 1993. http://dx.doi.org/10.23919/acc.1993.4793265.

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Fabien, Brian C. „Dynamic System Optimization Using Higher-Order Runge-Kutta Discretization“. In ASME 2010 International Mechanical Engineering Congress and Exposition. ASMEDC, 2010. http://dx.doi.org/10.1115/imece2010-39421.

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This paper evaluates some numerical methods for the approximate solution dynamic system optimization problems. The paper considers the optimization of dynamic systems that are subject to equality and inequality constraints. These types of problems include optimal control and parameter identification optimization problems. The numerical solution technique is based on transforming the infinite dimensional dynamic system optimization problem into a finite dimensional nonlinear programming (NLP) problem. This solution method is realized by; (i) approximating the control input using a finite set of parameters; (ii) approximating the differential equations using an explicit Runge-Kutta method; and (iii) solving the resultant NLP problem using a sequential quadratic programming method. The paper evaluates the efficacy of approximating the control input using (I) piecewise constants, (II) piecewise linear polynomials, or (III) piecewise cubic polynomials. In addition, the paper compares the performance of various Runge-Kutta methods of order 3 through 9.

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Fabien, Brian C. „Implementation of an Algorithm for the Direct Solution of Optimal Control Problems“. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2011. http://dx.doi.org/10.1115/detc2011-48750.

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This paper presents the implementation of a numerical algorithm for the direct solution of optimal control and parameter identification problems. The problems may include differential equations that define the state, inequality constraints, and equality constraints at the initial and final times. The numerical method is based on transforming the infinite dimensional optimal control problem into a finite dimensional nonlinear programming problem. The transformation technique involves dividing the time interval of interest into a mesh that need not be uniform. In each subinterval of the mesh the control input is approximated using a piecewise polynomial. In particular, the control can be approximated using: (i) piecewise constant, (ii) piecewise linear, or (iii) piecewise cubic polynomials. The explicit Runge-Kutta method is used to obtain an approximate solution of the differential equations that define the state. With the approach used here the states do not appear in the nonlinear programming (NLP) problem. As a result the NLP problem is very compact relative to other numerical methods used to solve nonlinear optimal control problems. The NLP problem is solved using a sequential quadratic programming (SQP) technique. The SQP method is based on minimizing the L1 exact penalty function. Each major step of the SQP method solves a strictly convex quadratic programming problem. The paper also describes a simplified interface to the computer programs that implement the method. An example is presented to demonstrate the algorithm.

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Saad, Hussein, Eduardo Divo, Sandra Boetcher, Jeff Brown und Alain Kassab. „A Robust and Efficient Thermographic NDE Tool Based on an Inverse VoF Meshless Method“. In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-36758.

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A novel computational tool based on the Localized Radial-basis Function (RBF) Collocation (LRC) Meshless method coupled with a Volume-of-Fluid (VoF) scheme capable of accurately and efficiently solving transient multi-dimensional heat conduction problems in composite and heterogeneous media is formulated and implemented. While the LRC Meshless method lends its inherent advantages of spectral convergence and ease of automation, the VoF scheme allows to effectively and efficiently simulate the location, size, and shape of cavities, voids, inclusions, defects, or de-attachments in the conducting media without the need to regenerate point distributions, boundaries, or interpolation matrices. To this end, the Inverse Geometric problem of Cavity Detection can be formulated as an optimization problem that minimizes an objective function that computes the deviation of measured temperatures at accessible locations to those generated by the LRC-VoF Meshless method. The LRC-VoF Meshless algorithms will be driven by an optimization code based on the Simplex Linear Programming algorithm which can efficiently search for the optimal set of design parameters (location, size, shape, etc.) within a predefined design space. Initial guesses to the search algorithm will be provided by the classical 1D semi-infinite composite analytical solution which can predict the approximate location but not the size or shape of the cavity. The LRC-VoF formulation is tested and validated through a series of controlled numerical experiments. The proposed approach will allow solving the onerous computational inverse geometric problem in a very efficient and robust manner while affording its implementation in modest computational platforms, thereby realizing the disruptive potential of the proposed multi-dimensional high-fidelity non-destructive evaluation (NDE) method in displacing the current practice of 1D-based NDE.

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