Honoring the Memory of C. Caratheodory (1873-1950)
Springer (ex-Kluwer) (2001), Nonconvex Optimization and Its Applications, Vol. 54, ISBN: 0-7923-6942-4
There has been much recent progress in
global optimization algorithms for nonconvex continuous and discrete problems
from both a theoretical and a practical perspective. Convex analysis plays a
fundamental role in the analysis and development of global optimization
algorithms. This is due to the fact that virtually all nonconvex 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 June 5-9, 2000
at Pythagorian, Samos, Greece. It was in honor of the memory of C. Caratheodory
(1873-1950). It was endorsed by the Mathematical Programming Society (MPS) and
by the Society for industrial and Applied Mathematics (SIAN) Activity Group in
Optimization.
This volume contains a selection of refereed papers based on invited and
contributing talks presented at the conference. The two themes of convexity and
global optimization pervade the book.
The conference provided a forum for researchers working on different aspects of
convexity and global optimization to present their recent discoveries, and to
interact with people working on complementary aspects of mathematical
programming.
| Preface | xi |
| Constantin Caratheodory: His Life and Work; C. Phili | xiii |
| 1. Inner Approximation of State-constrained Optimal Control Problems; F.H. Clarke, R.J. Stern | 1 |
| 2. Nonsmooth Problems in Mathematical Diagnostics; V.F. Demyanov, A. Astorino and M. Gaudioso | 11 |
| 3. Deterministic Global Optimization for Protein Structure Prediction; J.L. Klepeis, C.A. Floudas | 31 |
| 4. Some Remarks on Minimum Principles; F. Giannessi | 75 |
| 5. Transversal Hypergraphs and Families of Polyhedral Cones; L. Khachiyan | 105 |
| 6. SDP Relaxations in Combinatorial Optimization from a Lagrangian Viewpoint; C. Lemaréchal, F. Oustry | 119 |
| 7. Convex Analysis in the Calculus of Variations; R.T. Rockafellar | 135 |
| 8. Global Minimization and Parameter Estimation in Computational Biology; J.B. Rosen, A.T. Philips, S.Y. Oh and K.A. Dill | 153 |
| 9. Lagrangian Quadratic Bounds in Polynomial Nonconvex and Boolean Models with Superfluous Constraints; N.Z. Shor | 181 |
| 10. Generalized Duality in Variational Analysis; S.M. Robinson | 205 |
| 11. Clustering via D.C. Optimization; H. Tuy, A.M. Bagirov and A.M. Rubinov | 221 |
| 12. Algorithms and Merit Functions for the Principal Eigenvalue; G. Auchmuty | 235 |
| 13. Modified Versions of the Cutting Angle Method; A.M. Bagirov, A.M. Rubinov | 245 |
| 14. Theoretical and Computational Results for a Linear Bilevel Problem; M. Campelo, S. Scheimberg | 269 |
| 15. The Lagrangian Search Method; P.S. Efraimidis, P.G. Spirakis | 283 |
| 16. An epsilon-maximum Principle for Generalized Control Systems; A.H. Hamel | 295 |
| 17. D.C. Optimization Approaches via Markov Models for Restoration of Signal (1-D) and (2-D); L.T.H. An, P.D. Tao | 303 |
| 18. New Positive Semidefinite Relaxations for Nonconvex Quadratic Programs; J.B. Lasserre | 319 |
| 19. Interval Analysis Applied to Global Minimization; C. Lavor, N. Maculan | 333 |
| 20. Approximate Analytic Center Quadratic Cut Method for Strongly Monotone Variational Inequalities; H.J. Lüthi, B. Büeler | 345 |
| 21. Generating Convex Functions; P. Maréchal | 361 |
| 22. The Method of Moments for Nonconvex Variational Problems; R. Meziat, J.J. Egozcue and P. Pedregal | 371 |
| 23. A Pivoting-based Heuristic for the Maximum Clique Problem; A. Massaro, M. Pelillo | 383 |
| 24. An Analytic Center Self Concordant Cut Method for the Convex Feasibility Problem; F.S. Mokhtarian, J.L. Goffin | 395 |
| 25. Strengthened Semidefinite Programming Relaxations for the Max-Cut Problem; M.F. Anjos, H. Wolkowicz | 409 |
| 26. Supervised Training Using Global Search Methods; V.P. Plagianakos, G.D. Magoulas and M.N. Vrahatis | 421 |
| 27. Learning Rate Adaptation in Stochastic Gradient Descent; V.P. Plagianakos, G.D. Magoulas and M.N. Vrahatis | 433 |
| 28. Improving the Particle Swarm Optimizer by Function `Stretching'; K.E. Parsopoulos, V.P. Plagianakos, G.D. Magoulas and M.N. Vrahatis | 445 |
| 29. Some Convergence Properties of the Steepest Descent Algorithm Revealed by Renormalisation; L. Pronzato, H.P. Wynn and A.A. Zhigljiavsky | 459 |
| 30. Interior-Point Algorithm for Dantzig and Wolfe Decomposition Principle; M.A. dos Santos, P.R. Oliveira | 473 |
| 31. Stochastic Perturbation Methods for Affine Restrictions; M. Bouhadi, R. Ellaia and J.E. Souza de Cursi | 487 |
| 32. Directed Derivatives of Convex Compact-Valued Mappings; R. Baier, E.M. Farkhi | 501 |
| 33. A Perturbed Auxiliary Problem Method for Paramonotone Multivalued Mappings; G. Salmon, J.J.Strodiot and V.H. Nguyen | 515 |
| 34. A Nota on Random Variational Inequalities and Simple Random Unilateral Boundary Value Problems; J. Gwinner | 531 |
| 35. A Comparison Principle and the Lipschitz Continuity for Minimizers; C. Mariconda, G. Treu | 545 |
| 36. Tunneling and Genetic Algorithms for Global Optimization; S. Gómez, J. Solano, L. Castellanos and M.I. Quintana | 553 |
| 37. Convexity and Monotonicity in Global Optimization; H. Tuy | 569 |