Semi-Infinite Programming

Semi-infinite programming (SIP) deals with optimization problems in which either the number of decision variables or the number of constraints is finite. This book presents the state of the art in SIP in a suggestive way, bringing the powerful SIP tools close to the potential users in different scientific and technological fields. The volume is divided into four parts. Part I reviews the first decade of SIP (1962-1972). Part II analyses convex and generalised SIP, conic linear programming, and disjunctive programming. New numerical methods for linear, convex, and continuously differentiable SIP problems are proposed in Part III. Finally, Part IV provides an overview of the applications of SIP to probability, statistics, experimental design, robotics, optimization under uncertainty, production games, and separation problems. Audience: This book is an indispensable reference and source for advanced students and researchers in applied mathematics and engineering.

Inhalt

Preface. Contributing Authors. Part I: History. 1. On the 1962-1972 Decade of Semi-Infinite Programming: A Subjective View; K.O. Kortanek. Part II: Theory. 2. About Disjunctive Optimization; I.I. Eremin. 3. On Regularity and Optimality in Nonlinear Semi-Infinite Programming; A. Hassouni, W. Oettli. 4. Asymptotic Constraint Qualifications and Error Bounds for Semi-Infinite Systems of Convex Inequalities; W. Li, I. Singer. 5. Stability of the Feasible Set Mapping in Convex Semi-Infinite Programming; M.A. López, et al. 6. On Convex Lower Level Problems in Generalized Semi-Infinite Optimization; J.-J. Rückmann, O. Stein. 7. On Duality Theory of Conic Linear Problems; A. Shapiro. Part III: Numerical Methods. 8. Two Logarithmic Barrier Methods for Convex Semi-Infinite Problems; L. Abbe. 9. First-Order Algorithms for Optimization Problems with a Maximum Eigenvalue/Singular Value Cost and or Constraints; E. Polak. 10. Analytic Center Based Cutting Plane Method for Linear Semi-Infinite Programming; S.-Y. Wu, et al. Part IV: Modeling and Applications. 11. On Some Applications of LSIP to Probability and Statistics; M. Dall'Aglio. 12. Separation by Hyperplanes: A Linear Semi-Infinite Programming Approach; M.A. Goberna, et al. 13. A Semi-Infinite Optimization Approach to Optimal Spline Trajectory Planning of Mechanical Manipulators; C. Guarino Lo Bianco, A. Piazzi. 14. On Stability of Guaranteed Estimation Problems: Error Bounds for Information Domains and Experimental Design; M.I. Gusev, S.A.Romanov. 15. Optimization under Uncertainty and Linear Semi-Infinite Programming: A Survey; T. León, E. Vercher. 16. Semi-Infinite Assignment and Transportation Games; J. Sánchez-Soriano, et al. 17. The Owen Set and the Core of Semi-Infinite Linear Production Situations; S. Tijs, et al.