Semi-Infinite Programming: Recent Advances
Miguel Ángel Goberna, Marco A. López
Springer Science & Business Media, 2001. gada 31. okt. - 386 lappuses
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.
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ABOUT DISJUNCTIVE OPTIMIZATION
ERROR BOUNDS FOR SEMIINFINITE SYSTEMS
PROBLEMS WITH A MAXIMUM EIGENVALUE
ON SOME APPLICATIONS OF LSIP TO PROBABILITY
ON STABILITY OF GUARANTEED ESTIMATION
ON DUALITY THEORY OF CONIC LINEAR PROBLEMS
THE OWEN SET AND THE CORE OF SEMIINFINITE
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algorithm analysis Applications approach approximations assume assumption Banach space closed compact compute condition cone Consequently consider consistent constant constraints continuous Control convergence convex corresponding cutting defined definition denote dual duality equality equivalent error bound estimation example exists extended fact feasible finite function fuzzy given global Hence holds implies inequality inequality system infinite interval introduced iteration Journal known Lemma linear programming LSIP Mathematical means measure method minimizer nonempty norm Note obtain operator optimal optimal solution optimization problem parameter positive possible precision producers programming problems Proof proposed Proposition prove References Remark Research respectively result satisfied semi-infinite programming separating sequence situation solution solving space Step strong subset Suppose technique Theorem theory topology University vector weak