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1. |
Record Nr. |
UNINA9910780730603321 |
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Autore |
Lasserre Jean-Bernard <1953-> |
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Titolo |
Moments, positive polynomials and their applications [[electronic resource] /] / Jean-Bernard Lasserre |
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Pubbl/distr/stampa |
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London, : Imperial College Press, 2009 |
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ISBN |
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1-282-76000-9 |
9786612760006 |
1-84816-446-7 |
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Descrizione fisica |
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1 online resource (384 p.) |
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Collana |
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Imperial College Press optimization series, , 2041-1677 ; ; 1 |
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Disciplina |
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Soggetti |
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Moments method (Statistics) |
Polynomials |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Contents; Preface; Acknowledgments; Part I Moments and Positive Polynomials; 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-de nite 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; 2.5.1 Representations via sums of squares |
2.5.2 A matrix version of Putinar's Positivstellensatz2.5.3 An alternative representation; 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; 3.1.1 The full moment problem; 3.1.2 The truncated moment problem; 3.2 The Multi-dimensional Moment Problem; 3.2.1 Moment and localizing matrix; 3.2.2 Positive and at extensions of moment matrices; 3.3 The K-moment Problem; 3.4 Moment Conditions for Bounded Density |
3.4.1 The compact case3.4.2 The non compact case; 3.5 Summary; 3.6 Exercises; 3.7 Notes and Sources; 4. Algorithms for Moment Problems; 4.1 The Overall Approach; 4.2 Semide nite Relaxations; 4.3 Extraction |
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of Solutions; 4.4 Linear Relaxations; 4.5 Extensions; 4.5.1 Extensions to countably many moment constraints; 4.5.2 Extension to several measures; 4.6 Exploiting Sparsity; 4.6.1 Sparse semide nite relaxations; 4.6.2 Computational complexity; 4.7 Summary; 4.8 Exercises; 4.9 Notes and Sources; 4.10 Proofs; 4.10.1 Proof of Theorem 4.3; 4.10.2 Proof of Theorem 4.7; Part II Applications |
5. Global Optimization over Polynomials5.1 The Primal and Dual Perspectives; 5.2 Unconstrained Polynomial Optimization; 5.3 Constrained Polynomial Optimization: Semide nite Relaxations; 5.3.1 Obtaining global minimizers; 5.3.2 The univariate case; 5.3.3 Numerical experiments; 5.3.4 Exploiting sparsity; 5.4 Linear Programming Relaxations; 5.4.1 The case of a convex polytope; 5.4.2 Contrasting LP and semide nite relaxations.; 5.5 Global Optimality Conditions; 5.6 Convex Polynomial Programs; 5.6.1 An extension of Jensen's inequality; 5.6.2 The s.o.s.-convex case; 5.6.3 The strictly convex case |
5.7 Discrete Optimization5.7.1 Boolean optimization; 5.7.2 Back to unconstrained 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 Uni ed Treatment; 6.3.1 Basic underlying idea; 6.3.2 The moment-matrix algorithm; 6.4 Summary; 6.5 Exercises; 6.6 Notes and Sources; 7. Applications in Probability |
7.1 Upper Bounds on Measures with Moment Conditions |
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Sommario/riassunto |
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Many important applications in global optimization, algebra, probability and statistics, applied mathematics, control theory, financial mathematics, inverse problems, etc. can be modeled as a particular instance of the <i>Generalized Moment Problem (GMP)</i>. This book introduces a new general methodology to solve the GMP when its data are polynomials and basic semi-algebraic sets. This methodology combines semidefinite programming with recent results from real algebraic geometry to provide a hierarchy of semidefinite relaxations converging to the desired optimal value. Applied on appropriat |
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2. |
Record Nr. |
UNINA9910820721803321 |
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Autore |
Kutá̕ková Eva |
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Titolo |
Laudabile carmen . Část II Kapitoly z římské rétoriky a poetiky / / Eva Kut'áková |
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Pubbl/distr/stampa |
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[Place of publication not identified] : , : Karolinum, , 2017 |
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©2017 |
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ISBN |
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Edizione |
[Vydání první.] |
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Descrizione fisica |
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1 online resource (172 pages) |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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3. |
Record Nr. |
UNINA9910968011203321 |
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Autore |
Rolim Maria Helena Fonseca de Souza |
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Titolo |
The international law on ballast water : preventing biopollution / / by Maria Helena Fonseca de Souza Rolim ; with contributions by Erkki Leppakoski, Gaetano Librando |
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Pubbl/distr/stampa |
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Leiden ; ; Boston, : Martinus Nijhoff Publishers, 2008 |
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ISBN |
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1-282-39839-3 |
9786612398391 |
90-04-18078-8 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (424 p.) |
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Collana |
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Publications on ocean development, , 0924-1922 ; ; v. 63 |
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Altri autori (Persone) |
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LeppäkoskiErkki |
LibrandoGaetano |
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Disciplina |
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Soggetti |
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Marine pollution - Law and legislation |
Discharge of ballast water - Environmental aspects |
Nonindigenous aquatic pests - Control - Law and legislation |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Biopollution and ballast water -- Evolution of the international law on biopollution -- IMO and codification of the International Law on Ballast Water Management -- GloBallast legislative review : Brazilian case study. |
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Sommario/riassunto |
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\'The introduction of invasive marine species into new environments, whether by ships’ ballast water, attached to ships’ hulls or via other means has been identified as one of the four main threats to the world’s oceans, along with land-based sources of marine pollution, over-exploitation of living marine resources and the physical alteration or destruction of marine habitat. Increased trade and the consequent greater volumes of maritime traffic over the last few decades have served to fuel the problem. The effects in many areas of the world have been serious and significant. Quantitative data show that the rate of bio-invasions is continuing to increase, in some cases exponentially, and new areas are being found to be invaded all the time. As volumes of seaborne trade continue overall to increase, the problem may not yet have reached its peak. In response, IMO first adopted Guidelines for |
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Preventing the Introduction of Unwanted Organisms and Pathogens from Ships' Ballast Water and Sediment Discharges in 1991; while the United Nations Conference on Environment and Development (UNCED), held in Rio de Janeiro in 1992, recognized the issue as a major international concern. The IMO Guidelines have since been kept constantly under review and updated. Subsequently, in February 2004, the International Convention for the Control and Management of Ships’ Ballast Water and Sediments was adopted. In providing a broad overview of the legal aspects related to marine pollution caused by ballast water and tank sediments, this book offers a pragmatic analysis of the current international legal system, and includes principles of international customary law and also references to a comprehensive environmental treaty law framework which relates the Ballast Water Convention to other treaties, such as the United Nations Convention on the Law of the Sea (UNCLOS), MARPOL and the Convention on Biological Diversity. With such a wide-ranging approach, this book will certainly provide a source of valuable information for all those with a requirement to pursue the subject in depth.\' From the Foreword by Efthimios E. Mitropoulos |
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