Jean Bernard Lasserre's Books

An Introduction to Polynomial and Semi-Algebraic Optimization

By: Jean Bernard Lasserre

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An Introduction to Polynomial and Semi-Algebraic Optimization

By: Jean Bernard Lasserre

The first comprehensive introduction to the powerful moment approach for solving global optimization problems.

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355

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Cambridge University Press

Published Date

ISBN 10

1107060575

ISBN 13

9781107060579

An Introduction to Polynomial and Semi-Algebraic Optimization

By: Jean Bernard Lasserre

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An Introduction to Polynomial and Semi-Algebraic Optimization

By: Jean Bernard Lasserre

The first comprehensive introduction to the powerful moment approach for solving global optimization problems.

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355

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Cambridge University Press

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ISBN 10

1107060575

ISBN 13

9781107060579

Markov Chains and Invariant Probabilities

By: Onésimo Hernández-Lerma,Jean B. Lasserre

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Markov Chains and Invariant Probabilities

By: Onésimo Hernández-Lerma,Jean B. Lasserre

This book is about discrete-time, time-homogeneous, Markov chains (Mes) and their ergodic behavior. To this end, most of the material is in fact about stable Mes, by which we mean Mes that admit an invariant probability measure. To state this more precisely and give an overview of the questions we shall be dealing with, we will first introduce some notation and terminology. Let (X,B) be a measurable space, and consider a X-valued Markov chain ~. = {~k' k = 0, 1, ... } with transition probability function (t.pJ.) P(x, B), i.e., P(x, B) := Prob (~k+1 E B I ~k = x) for each x E X, B E B, and k = 0,1, .... The Me ~. is said to be stable if there exists a probability measure (p.m.) /.l on B such that (*) VB EB. /.l(B) = Ix /.l(dx) P(x, B) If (*) holds then /.l is called an invariant p.m. for the Me ~. (or the t.p.f. P).

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Page Count

213

Publisher

Birkhäuser

Published Date

ISBN 10

3034880243

ISBN 13

9783034880244

Moment-sos Hierarchy, The: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear Pdes

By: Didier Henrion,Milan Korda,Jean Bernard Lasserre

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Moment-sos Hierarchy, The: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear Pdes

By: Didier Henrion,Milan Korda,Jean Bernard Lasserre

The Moment-SOS hierarchy is a powerful methodology that is used to solve the Generalized Moment Problem (GMP) where the list of applications in various areas of Science and Engineering is almost endless. Initially designed for solving polynomial optimization problems (the simplest example of the GMP), it applies to solving any instance of the GMP whose description only involves semi-algebraic functions and sets. It consists of solving a sequence (a hierarchy) of convex relaxations of the initial problem, and each convex relaxation is a semidefinite program whose size increases in the hierarchy.The goal of this book is to describe in a unified and detailed manner how this methodology applies to solving various problems in different areas ranging from Optimization, Probability, Statistics, Signal Processing, Computational Geometry, Control, Optimal Control and Analysis of a certain class of nonlinear PDEs. For each application, this unconventional methodology differs from traditional approaches and provides an unusual viewpoint. Each chapter is devoted to a particular application, where the methodology is thoroughly described and illustrated on some appropriate examples.The exposition is kept at an appropriate level of detail to aid the different levels of readers not necessarily familiar with these tools, to better know and understand this methodology.

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248

Publisher

World Scientific

Published Date

ISBN 10

1786348551

ISBN 13

9781786348555

Further Topics on Discrete-Time Markov Control Processes

By: Onesimo Hernandez-Lerma,Jean B. Lasserre

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Further Topics on Discrete-Time Markov Control Processes

By: Onesimo Hernandez-Lerma,Jean B. Lasserre

Devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes, the text is mainly confined to MCPs with Borel state and control spaces. Although the book follows on from the author's earlier work, an important feature of this volume is that it is self-contained and can thus be read independently of the first. The control model studied is sufficiently general to include virtually all the usual discrete-time stochastic control models that appear in applications to engineering, economics, mathematical population processes, operations research, and management science.

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Page Count

286

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461205611

ISBN 13

9781461205616

The Christoffel–Darboux Kernel for Data Analysis

By: Jean Bernard Lasserre,Edouard Pauwels,Mihai Putinar

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The Christoffel–Darboux Kernel for Data Analysis

By: Jean Bernard Lasserre,Edouard Pauwels,Mihai Putinar

This accessible overview introduces the Christoffel-Darboux kernel as a novel, simple and efficient tool in statistical data analysis.

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185

Publisher

Cambridge University Press

Published Date

ISBN 10

1108838065

ISBN 13

9781108838061

An Integrated Approach in Production Planning and Scheduling

By: Stephane Dauzere-Peres,Jean-Bernard Lasserre

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An Integrated Approach in Production Planning and Scheduling

By: Stephane Dauzere-Peres,Jean-Bernard Lasserre

Production Management is a large field concerned with all the aspects related to production, from the very bottom decisions at the machine level, to the top-level strategic decisicns. In this book, we are concerned with production planning and scheduling aspects. Traditional production planning methodologies are based on a now widely ac cepted hierarchical decom?osition into several planning decision levels. The higher in the hierarchy, the more aggregate are the models and the more important are the decisions. In this book, we only consider the last two decision levels in the hierarchy, namely, the mid-term (or tacticaQ planning level and the short-term (or operationaQ scheduling level. In the literature and in practice, the decisions are taken in sequence and in a top-down approach from the highest level in the hierarchy to the bottom level. The decisions taken at some level in the hierarchy are constrained by those already taken at upper levels and in turn, must translate into feasible objectives for the next lower levels in the hierarchy. It is a common sense remark to say that the whole hierarchical decision process is coherent if the interactions between different levels in the hierarchy are taken into account so that a decision taken at some level in the hierarchy translates into a feasible objective for the next decision level in the hierarchy. However, and surpris ingly enough, this crucial consistency issue is rarely investigated and few results are available in the literature.

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154

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642468047

ISBN 13

9783642468049

Geometric and Topological Inference

By: Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec

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Geometric and Topological Inference

By: Jean-Daniel Boissonnat,Frédéric Chazal,Mariette Yvinec

Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.

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247

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Cambridge University Press

Published Date

ISBN 10

1108317618

ISBN 13

9781108317610

Linear and Integer Programming vs Linear Integration and Counting

A Duality Viewpoint

By: Jean-Bernard Lasserre

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Linear and Integer Programming vs Linear Integration and Counting

A Duality Viewpoint

By: Jean-Bernard Lasserre

This book analyzes and compares four closely related problems, namely linear programming, integer programming, linear integration, and linear summation (or counting). The book provides some new insights on duality concepts for integer programs.

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Page Count

167

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387094148

ISBN 13

9780387094144

Moments, Positive Polynomials and Their Applications

By: Jean-Bernard Lasserre

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Moments, Positive Polynomials and Their Applications

By: Jean-Bernard Lasserre

1. The generalized moment problem. 1.1. Formulations. 1.2. Duality theory. 1.3. Computational complexity. 1.4. Summary. 1.5. Exercises. 1.6. Notes and sources -- 2. Positive polynomials. 2.1. Sum of squares representations and semi-definite optimization. 2.2. Nonnegative versus s.o.s. polynomials. 2.3. Representation theorems : univariate case. 2.4. Representation theorems : mutivariate case. 2.5. Polynomials positive on a compact basic semi-algebraic set. 2.6. Polynomials nonnegative on real varieties. 2.7. Representations with sparsity properties. 2.8. Representation of convex polynomials. 2.9. Summary. 2.10. Exercises. 2.11. Notes and sources -- 3. Moments. 3.1. The one-dimensional moment problem. 3.2. The multi-dimensional moment problem. 3.3. The K-moment problem. 3.4. Moment conditions for bounded density. 3.5. Summary. 3.6. Exercises. 3.7. Notes and sources -- 4. Algorithms for moment problems. 4.1. The overall approach. 4.2. Semidefinite relaxations. 4.3. Extraction of solutions. 4.4. Linear relaxations. 4.5. Extensions. 4.6. Exploiting sparsity. 4.7. Summary. 4.8. Exercises. 4.9. Notes and sources. 4.10. Proofs -- 5. Global optimization over polynomials. 5.1. The primal and dual perspectives. 5.2. Unconstrained polynomial optimization. 5.3. Constrained polynomial optimization : semidefinite relaxations. 5.4. Linear programming relaxations. 5.5. Global optimality conditions. 5.6. Convex polynomial programs. 5.7. Discrete optimization. 5.8. Global minimization of a rational function. 5.9. Exploiting symmetry. 5.10. Summary. 5.11. Exercises. 5.12. Notes and sources -- 6. Systems of polynomial equations. 6.1. Introduction. 6.2. Finding a real solution to systems of polynomial equations. 6.3. Finding all complex and/or all real solutions : a unified treatment. 6.4. Summary. 6.5. Exercises. 6.6. Notes and sources -- 7. Applications in probability. 7.1. Upper bounds on measures with moment conditions. 7.2. Measuring basic semi-algebraic sets. 7.3. Measures with given marginals. 7.4. Summary. 7.5. Exercises. 7.6. Notes and sources -- 8. Markov chains applications. 8.1. Bounds on invariant measures. 8.2. Evaluation of ergodic criteria. 8.3. Summary. 8.4. Exercises. 8.5. Notes and sources -- 9. Application in mathematical finance. 9.1. Option pricing with moment information. 9.2. Option pricing with a dynamic model. 9.3. Summary. 9.4. Notes and sources -- 10. Application in control. 10.1. Introduction. 10.2. Weak formulation of optimal control problems. 10.3. Semidefinite relaxations for the OCP. 10.4. Summary. 10.5. Notes and sources -- 11. Convex envelope and representation of convex sets. 11.1. The convex envelope of a rational function. 11.2. Semidefinite representation of convex sets. 11.3. Algebraic certificates of convexity. 11.4. Summary. 11.5. Exercises. 11.6. Notes and sources -- 12. Multivariate integration 12.1. Integration of a rational function. 12.2. Integration of exponentials of polynomials. 12.3. Maximum entropy estimation. 12.4. Summary. 12.5. Exercises. 12.6. Notes and sources -- 13. Min-max problems and Nash equilibria. 13.1. Robust polynomial optimization. 13.2. Minimizing the sup of finitely many rational cunctions. 13.3. Application to Nash equilibria. 13.4. Exercises. 13.5. Notes and sources -- 14. Bounds on linear PDE. 14.1. Linear partial differential equations. 14.2. Notes and sources

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Page Count

384

Publisher

World Scientific

Published Date

ISBN 10

1848164467

ISBN 13

9781848164468

Discrete-Time Markov Control Processes

Basic Optimality Criteria

By: Onesimo Hernandez-Lerma,Jean B. Lasserre

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Discrete-Time Markov Control Processes

Basic Optimality Criteria

By: Onesimo Hernandez-Lerma,Jean B. Lasserre

This book presents the first part of a planned two-volume series devoted to a systematic exposition of some recent developments in the theory of discrete-time Markov control processes (MCPs). Interest is mainly confined to MCPs with Borel state and control (or action) spaces, and possibly unbounded costs and noncompact control constraint sets. MCPs are a class of stochastic control problems, also known as Markov decision processes, controlled Markov processes, or stochastic dynamic pro grams; sometimes, particularly when the state space is a countable set, they are also called Markov decision (or controlled Markov) chains. Regardless of the name used, MCPs appear in many fields, for example, engineering, economics, operations research, statistics, renewable and nonrenewable re source management, (control of) epidemics, etc. However, most of the lit erature (say, at least 90%) is concentrated on MCPs for which (a) the state space is a countable set, and/or (b) the costs-per-stage are bounded, and/or (c) the control constraint sets are compact. But curiously enough, the most widely used control model in engineering and economics--namely the LQ (Linear system/Quadratic cost) model-satisfies none of these conditions. Moreover, when dealing with "partially observable" systems) a standard approach is to transform them into equivalent "completely observable" sys tems in a larger state space (in fact, a space of probability measures), which is uncountable even if the original state process is finite-valued.

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