This volume contains the refereed proceedings of the special session on Optimization and Nonlinear Analysis held at the Joint American Mathematical Society-Israel Mathematical Union Meeting which took place at the Hebrew University of Jerusalem in May 1995. Most of the papers in this book originated from the lectures delivered at this special session. In addition, some participants who did not present lectures and invited speakers who were unable to attend contributed their work. The fields of optimization theory and nonlinear analysis continue to be very active. This book presents not only the wide spectrum and diversity of the results, but also their manifold connections to other areas, such as differential equations, functional analysis, operator theory, calculus of variations, numerical analysis, and mathematical programming. In reading this book one encounters papers that deal, for example, with convex, quasiconvex and generalized convex functions, fixed and periodic points, fractional-linear transformations, moduli of convexity, monotone operators, Morse lemmas, Navier-Stokes equations, nonexpansive maps, nonsmooth analysis, numerical stability, products of projections, steepest descent, the Leray-Schauder degree, the turnpike property, and variational inequalities.

Introduction.

H. H. Bauschke, J. M. Borwein, and A. S. Lewis -- The method of cyclic projections for closed convex sets in Hilbert space

A. Ben-Israel -- Newton's method with modified functions

Bjck -- Numerical stability of methods for solving augmented systems

D. Butnariu and A. N. Iusem -- Local moduli of convexity and their application to finding almost common fixed points of measurable families of operators

F. H. Clarke, Y. S. Ledyaev, and R. J. Stern -- Fixed point theory via nonsmooth analysis

Z. Guan and A. G. Kartsatos -- Ranges of generalized pseudo-monotone perturbations of maximal monotone operators in reflexive Banach spaces

M. J. Holst and E. S. Titi -- Determining projections and functionals for weak solutions of the Navier-Stokes equations

A. Ioffe and E. Schwartzman -- Parametric Morse lemmas for $C^{1,1}$-functions

V. Khatskevich and L. Zelenko -- The fractional-linear transformations of the operator ball and dichotomy of solutions to evolution equations

M. Z. Nashed and O. Scherzer -- Stable approximation of nondifferentiable optimization problems with variational inequalities

J. W. Neuberger -- Sobolev gradients and boundary conditions for partial differential equations

R. D. Nussbaum -- A nonlinear generalization of Perron-Frobenius theory and periodic points of nonexpansive maps

A. M. Rubinov and B. M. Glover -- On generalized quasiconvex conjugation

S. Simons -- Subdifferentials of convex functions

A. J. Zaslavski -- Existence and structure of optimal solutions of variational problems

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