From one of the 20th century’s most profound philosophers and writers, comes a thought provoking essay that seeks to reconcile Marxism with existentialism. Exploring the complicated relationship the two philosophical schools of thought have with one another, Sartre supposes that the two are in fact compatible and complimentary towards one another, with poignant analysis and reasoning. An important work of modern philosophy, Search for a Method has a major influence on the current perceptions of existentialism and Marxism. “This is the most important philosophical work by Sartre to be translated since Being and Nothingness.”—James Collings, America

An infinite number of mathematical models can be created to describe naturally occurring physical systems. In addition there is a smaller, but large, number of criteria which can be used to measure the goodness of fit of a model to a physical process. Together, a selected criterion and a mathematical model define an objective function to be optimized.

The book is intended for graduate students and researchers in mathematics, computer science, and operational research. The book presents a new derivative-free optimization method/algorithm based on randomly generated trial points in specified domains and where the best ones are selected at each iteration by using a number of rules. This method is different from many other well established methods presented in the literature and proves to be competitive for solving many unconstrained optimization problems with different structures and complexities, with a relative large number of variables. Intensive numerical experiments with 140 unconstrained optimization problems, with up to 500 variables, have shown that this approach is efficient and robust. Structured into 4 chapters, Chapter 1 is introductory. Chapter 2 is dedicated to presenting a two level derivative-free random search method for unconstrained optimization. It is assumed that the minimizing function is continuous, lower bounded and its minimum value is known. Chapter 3 proves the convergence of the algorithm. In Chapter 4, the numerical performances of the algorithm are shown for solving 140 unconstrained optimization problems, out of which 16 are real applications. This shows that the optimization process has two phases: the reduction phase and the stalling one. Finally, the performances of the algorithm for solving a number of 30 large-scale unconstrained optimization problems up to 500 variables are presented. These numerical results show that this approach based on the two level random search method for unconstrained optimization is able to solve a large diversity of problems with different structures and complexities. There are a number of open problems which refer to the following aspects: the selection of the number of trial or the number of the local trial points, the selection of the bounds of the domains where the trial points and the local trial points are randomly generated and a criterion for initiating the line search.

Rene Descartes credited his success in philosophy, mathematics, and physics to the discovery of a universal method of inquiry, but he provided no systematic description of his method. Descartes and Method carefully examines Descartes' scattered remarks on his application and puts forward a systematic account of his method with particular attention to the role it plays in the Meditations. Daniel E. Flage and Clarence A. Bonnen boldly and convincingly argue against the orthodox conception that Descartes had no method. Through a rigorous and thorough examination, Flage and Bonnen unearth and explain the role of the method of analysis in the Meditations. Descartes and Method is a ground-breaking book that is sure to make a considerable impact on the philosophy community. Anyone wishing to gain a new understanding of Descartes's Meditations should read this book.

In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Naviet-Stokes equations represent the extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum. We formulate the conditions of reaching this extremum, which are at the same time necessary and sufficient conditions of this functional global extremum existence.