Advances in Convex Analysis and Global Optimization

There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming.

Klappentext

There has been much recent progress in global optimization algo­ rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun­ damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon­ vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en­ dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech­ nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut­ ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti­ mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming.

Inhalt

1. Inner Approximation of State-constrained Optimal Control Problems.- 2. Nonsmooth Problems in Mathematical Diagnostics.- 3. Deterministic Global Optimization for Protein Structure Prediction.- 4. Some Remarks on Minimum Principles.- 5. Transversal Hypergraphs and Families of Polyhedral Cones.- 6. SDP Relaxations in Combinatorial Optimization from a Lagrangian Viewpoint.- 7. Convex Analysis in the Calculus of Variations.- 8. Global Minimization and Parameter Estimation in Computational Biology.- 9. Lagrangian Quadratic Bounds in Polynomial Nonconvex and Boolean Models with Superfluous Constraints.- 10. Generalized Duality in Variational Analysis.- 11. Clustering via D. C. Optimization.- 12. Algorithms and Merit Functions for the Principal Eigen-value.- 13. Modified Versions of the Cutting Angle Method.- 14. Theoretical and Computational Results for a Linear Bilevel Problem.- 15. The Lagrangian Search Method.- 16. An ?maximum Principle for Generalized Control Systems.- 17. D.C. Optimization Approaches via Markov Models for Restoration of Signal (1-D) and (2-D).- 18. New Positive Semidefinite Relaxations for Nonconvex Quadratic Programs.- 19. Interval Analysis Applied to Global Minimization.- 20. Approximate Analytic Center Quadratic Cut Method for Strongly Monotone Variational Inequalities.- 21. Generating Convex Functions.- 22. The Method of Moments for Nonconvex Variational Problems.- 23. A Pivoting-based Heuristic for the Maximum Clique Problem.- 24. An Analytic Center Self Concordant Cut Method for the Convex Feasibility Problem.- 25. Strengthened Semidefinite Programming Relaxations for the Max-Cut Problem.- 26. Supervised Training Using Global Search Methods.- 27. Learning Rate Adaptation in Stochastic Gradient Descent.- 28. Improving the Particle SwarmOptimizer by Function Stretching.- 29. Some Convergence Properties of the Steepest Descent Algorithm Revealed by Renormalisation.- 30. InteriorPoint Algorithm for Dantzig and Wolfe Decomposition Principle.- 31. Stochastic Perturbation Methods for Affine Restrictions.- 32. Directed Derivatives of Convex Compact-Valued Mappings.- 33. A Perturbed Auxiliary Problem Method for Paramonotone Multivalued Mappings.- 34. A Note on Random Variational Inequalities and Simple Random Unilateral Boundary Value Problems.- 35. A Comparison Principle and the Lipschitz Continuity for Minimizers.- 36. Tunneling and Genetic Algorithms for Global Optimization.- 37. Convexity and Monotonicity in Global Optimization.