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Nonlinear Optimization in Finite Dimensions
At the heart of the topology of global optimization lies Morse Theory: The study of the behaviour of lower level sets of functions as the level varies. Roughly speaking, the topology of lower level sets only may change when passing a level which corresponds to a stationary point (or Karush-Kuhn Tucker point). We study elements of Morse Theory, both in the unconstrained and constrained case. Special attention is paid to the degree of differentiabil ity of the functions under consideration. The reader will become motivated to discuss the possible shapes and forms of functions that may possibly arise within a given problem framework. In a separate chapter we show how certain ideas may be carrie...
Nonlinear Optimization in IRN: Transversality, flows, parametric aspects
In this second volume we pay attention to three important subjects in nonlinear optimization. The first one concerns the dependence of an optimization problem on the problem data: stability, resp. sensitivity aspects are considered from both a local and global point of view. Since stability results are intimately related with some concepts of transversality, we treat transversality theory in detail. A second subject consists on one hand of gradients, the gradient differential equation and its use in the search for several local minima. On the other hand we treat the underlying differential equation for Newton's method for finding critical points of a function. Again, transversality plays a crucial role. Finally, we consider optimization problems depending on parameters (critical sets, bifurcation of the feasible set, etc.) The present volume is preceded by a first one in which we study manifolds with boundary and critical point theory (Morse theory) within the framework of nonlinear optimization.
Twilight
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Topics in Engineering Mathematics
This volume presents a selection of expository papers on various topics in engineering mathematics. The papers concern model problems relating to, amongst others, the automobile and shipping industries, transportation networks and wave propagation. Among the methods treated are numerical methods, such as the finite element method and Newton's method, Karmarkar's interior point method and generalizations, and recurrence and induction in computer science. This volume will be of great interest to applied mathematicians, physicists and engineers interested in recent developments in engineering mathematics. The papers are written with an emphasis on exposition and should be accessible to all members of scientific community interested in modeling and solving real-life problems.
The Last Knight
There may not be a more fascinating a historical period than the late fourteenth century in Europe. The Hundred Years' War ravaged the continent, yet gallantry, chivalry, and literary brilliance flourished in the courts of England and elsewhere. It was a world in transition, soon to be replaced by the Renaissance and the Age of Exploration -- and John of Gaunt was its central figure. In today's terms, John of Gaunt was a multibillionaire with a brand name equal to Rockefeller. He fought in the Hundred Years' War, sponsored Chaucer and proto-Protestant religious thinkers, and survived the dramatic Peasants' Revolt, during which his sumptuous London residence was burned to the ground. As head of the Lancastrian branch of the Plantagenet family, Gaunt was the unknowing father of the War of the Roses; after his death, his son usurped the crown from his nephew, Richard II. Gaunt's adventures represent the culture and mores of the Middle Ages as those of few others do, and his death is portrayed in The Last Knight as the end of that enthralling period.
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.
