Rigorous Global Search Continuous Problems

Rigorous Global Search  Continuous Problems

In principle, global optima can be found by computing roots of the Fritz John conditions presented in $5.2.5 below. (Such roots represent critical points of the constrained problem.) However, merely finding critical points ignores much ...

Author: R. Baker Kearfott

Publisher: Springer Science & Business Media

ISBN: 9781475724950

Category: Mathematics

Page: 264

View: 275

This work grew out of several years of research, graduate seminars and talks on the subject. It was motivated by a desire to make the technology accessible to those who most needed it or could most use it. It is meant to be a self-contained introduction, a reference for the techniques, and a guide to the literature for the underlying theory. It contains pointers to fertile areas for future research. It also serves as introductory documentation for a Fortran 90 software package for nonlinear systems and global optimization. The subject of the monograph is deterministic, automatically verified or r- orous methods. In such methods, directed rounding and computational fix- point theory are combined with exhaustive search (branch and bound) te- niques. Completion of such an algorithm with a list of solutions constitutes a rigorous mathematical proof that all of the solutions within the original search region are within the output list. The monograph is appropriate as an introduction to research and technology in the area, as a desk reference, or as a graduate-level course reference. Kno- edge of calculus, linear algebra, and elementary numerical analysis is assumed.
Categories: Mathematics

Encyclopedia of Optimization

Encyclopedia of Optimization

Corliss GF, Kearfott RB (1998) Rigorous global search: Industrial applications. In: Csendes T (ed) (Special issues of the journal 'Reliable Computing'). ... Kearfott RB (1996) Rigorous global search: Continuous problems.

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

ISBN: 9780387747583

Category: Mathematics

Page: 4622

View: 181

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".
Categories: Mathematics

Global Optimization and Constraint Satisfaction

Global Optimization and Constraint Satisfaction

On verifying feasiblility in equality constrained optimization problems. Technical report, Deptartment of Mathematics, Univ. of Southwestern Louisiana, 1994. 61 [7] R.B. Kearfott. Rigorous Global Search: Continuous Problems.

Author: Christian Bliek

Publisher: Springer

ISBN: 9783540399018

Category: Mathematics

Page: 248

View: 221

This book constitutes the thoroughly refereed post-proceedings of the First International Workshop on Global Constraints Optimization and Costraint Satisfaction, COCOS 2002, held in Valbonne-Sophia Antipolis, France in October 2002. The 15 revised full papers presented together with 2 invited papers were carefully selected during two rounds of reviewing and improvement. The papers address current issues in global optimization, mathematical programming, and constraint programming; they are grouped in topical sections on optimization, constraint satisfaction, and benchmarking.
Categories: Mathematics

Global Optimization and Constraint Satisfaction

Global Optimization and Constraint Satisfaction

Second International Workshop, COCOS 2003, Lausanne, Switzerland, Nevember 18-21, 2003, Revised Selected Papers Christophe ... Kearfott R. B. (1996), “Rigorous Global Search: Continuous Problems,” Series Nonconvex Optimization and its ...

Author: Christophe Jermann

Publisher: Springer

ISBN: 9783540320418

Category: Computers

Page: 193

View: 281

Theformulationofmanypracticalproblemsnaturallyinvolvesconstraintsonthe variables entering the mathematical model of a real-life situation to be analyzed. It is of great interest to ?nd the possible scenarios satisfying all constraints, and, iftherearemanyofthem,eitherto?ndthebestsolution,ortoobtainacompact, explicit representation of the whole feasible set. The 2nd Workshop on Global Constrained Optimization and Constraint S- isfaction, COCOS 2003, which took place during November 18–21, 2003 in L- sanne, Switzerland, was dedicated to theoretical, algorithmic, and application oriented advances in answering these questions. Here global optimization refers to ?nding the absolutely best feasible point, while constraint satisfaction refers to?ndingallpossiblefeasiblepoints.AsinCOCOS2002,the?rstsuchworkshop (see the proceeedings [1]), the emphasis was on complete solving techniques for problems involving continuous variables that provide all solutions with full rigor, and on applications which, however, were allowed to have relaxed standards of rigor. The participants used the opportunity to meet experts from global optimi- tion, mathematical programming, constraint programming, and applications, and to present and discuss ongoing work and new directions in the ?eld. Four invited lectures and 20 contributed talks were presented at the workshop. The invited lectures were given by John Hooker (Logic-Based Methods for Global Optimization), Jean-Pierre Merlet (Usual and Unusual Applications of Interval Analysis), Hermann Schichl (The COCONUT Optimization Environment), and Jorge Mor ́ e (Global Optimization Computational Servers). This volume contains the text of Hooker’s invited lecture and of 12 c- tributed talks. Copies of the slides for most presentations can be found at [2]. Constraintsatisfactionproblems.Threepapersfocusonalgorithmicaspects of constraint satisfaction problems.
Categories: Computers

Modeling and Optimization in Space Engineering

Modeling and Optimization in Space Engineering

... Berlin (1996) Kearfott, R.B.: Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht (1996) to Discrete and Global Optimization. Kluwer, Dordrecht (1996) Floudas, C.A., Pardalos, P.M., Adjiman, C., Esposito, W.R., G€um€us, ...

Author: Giorgio Fasano

Publisher: Springer Science & Business Media

ISBN: 9781461444695

Category: Mathematics

Page: 404

View: 840

This volume presents a selection of advanced case studies that address a substantial range of issues and challenges arising in space engineering. The contributing authors are well-recognized researchers and practitioners in space engineering and in applied optimization. The key mathematical modeling and numerical solution aspects of each application case study are presented in sufficient detail. Classic and more recent space engineering problems – including cargo accommodation and object placement, flight control of satellites, integrated design and trajectory optimization, interplanetary transfers with deep space manoeuvres, low energy transfers, magnetic cleanliness modeling, propulsion system design, sensor system placement, systems engineering, space traffic logistics, and trajectory optimization – are discussed. Novel points of view related to computational global optimization and optimal control, and to multidisciplinary design optimization are also given proper emphasis. A particular attention is paid also to scenarios expected in the context of future interplanetary explorations. Modeling and Optimization in Space Engineering will benefit researchers and practitioners working on space engineering applications. Academics, graduate and post-graduate students in the fields of aerospace and other engineering, applied mathematics, operations research and optimal control will also find the book useful, since it discusses a range of advanced model development and solution techniques and tools in the context of real-world applications and new challenges.
Categories: Mathematics

Advances in Metaheuristics for Hard Optimization

Advances in Metaheuristics for Hard Optimization

Proceedings of the First IEEE International Conference on Evolutionary Computation, IEEE Press. 579–584 Kearfott R B (1996a) Rigorous Global Search: Continuous Problems. Kluwer, Dordrecht, Netherlands Kearfott R B (1996b) A Review of ...

Author: Patrick Siarry

Publisher: Springer Science & Business Media

ISBN: 9783540729600

Category: Mathematics

Page: 481

View: 205

Many advances have recently been made in metaheuristic methods, from theory to applications. The editors, both leading experts in this field, have assembled a team of researchers to contribute 21 chapters organized into parts on simulated annealing, tabu search, ant colony algorithms, general purpose studies of evolutionary algorithms, applications of evolutionary algorithms, and metaheuristics.
Categories: Mathematics

The GLOBAL Optimization Algorithm

The GLOBAL Optimization Algorithm

Last accessed July 2015 JScience: http://jscience.org (2017) JSGL: http://jgsl.sourceforge.net (2017) JQuantLib: http://www.jquantlib.org (2017) Kearfott, R.B.: Rigorous Global Search: Continuous Problems.

Author: Balázs Bánhelyi

Publisher: Springer

ISBN: 9783030023751

Category: Mathematics

Page: 111

View: 531

This book explores the updated version of the GLOBAL algorithm which contains improvements for a local search algorithm and new Java implementations. Efficiency comparisons to earlier versions and on the increased speed achieved by the parallelization, are detailed. Examples are provided for students as well as researchers and practitioners in optimization, operations research, and mathematics to compose their own scripts with ease. A GLOBAL manual is presented in the appendix to assist new users with modules and test functions. GLOBAL is a successful stochastic multistart global optimization algorithm that has passed several computational tests, and is efficient and reliable for small to medium dimensional global optimization problems. The algorithm uses clustering to ensure efficiency and is modular in regard to the two local search methods it starts with, but it can also easily apply other local techniques. The strength of this algorithm lies in its reliability and adaptive algorithm parameters. The GLOBAL algorithm is free to download also in the earlier Fortran, C, and MATLAB implementations.
Categories: Mathematics

Principles and Practice of Constraint Programming

Principles and Practice of Constraint Programming

21st International Conference, CP 2015, Cork, Ireland, August 31 -- September 4, 2015, Proceedings Gilles Pesant ... Dekker (1992) Kearfott, R.B.: Rigorous global search: continuous problems. Springer (1996) Leroy, X., Doligez, D., ...

Author: Gilles Pesant

Publisher: Springer

ISBN: 9783319232195

Category: Mathematics

Page: 747

View: 548

This book constitutes the refereed conference proceedings of the 21st International Conference on Principles and Practice of Constraint Programming, CP 2015, held in Cork, Ireland, in August/September 2015. This edition of the conference was part of George Boole 200, a celebration of the life and work of George Boole who was born in 1815 and worked at the University College of Cork. It was also co-located with the 31st International Conference on Logic Programming (ICLP 2015). The 48 revised papers presented together with 3 invited talks and 16 abstract papers were carefully selected from numerous submissions. The scope of CP 2014 includes all aspects of computing with constraints, including theory, algorithms, environments, languages, models, systems, and applications such as decision making, resource allocation, schedulling, configuration, and planning.
Categories: Mathematics

Handbook of Global Optimization

Handbook of Global Optimization

Coupling Genetic Algorithm with a Grid Search Method to Solve Mixed Integer Nonlinear Programming Problems. Comput. Math. ... Rigorous Global Search: Continuous Problems, volume 13 of Nonconvex Optimization and Its Applications.

Author: Panos M. Pardalos

Publisher: Springer Science & Business Media

ISBN: 9781475753622

Category: Mathematics

Page: 572

View: 980

In 1995 the Handbook of Global Optimization (first volume), edited by R. Horst, and P.M. Pardalos, was published. This second volume of the Handbook of Global Optimization is comprised of chapters dealing with modern approaches to global optimization, including different types of heuristics. Topics covered in the handbook include various metaheuristics, such as simulated annealing, genetic algorithms, neural networks, taboo search, shake-and-bake methods, and deformation methods. In addition, the book contains chapters on new exact stochastic and deterministic approaches to continuous and mixed-integer global optimization, such as stochastic adaptive search, two-phase methods, branch-and-bound methods with new relaxation and branching strategies, algorithms based on local optimization, and dynamical search. Finally, the book contains chapters on experimental analysis of algorithms and software, test problems, and applications.
Categories: Mathematics