This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "G. Stampacchia" School of Mathematics of the "E. Majorana" Centre for Scientific Culture, June 23 -July 2, 1998. In the tradition of these meetings, the main purpose was to review and discuss recent advances and promising research trends concerning theory, algorithms and innovative applications in the field of Nonlinear Optimization, and of related topics such as Convex Optimization, Nonsmooth Optimization, Variational Inequalities and Complementarity Problems. The meeting was attended by 83 people from 21 countries. Besides the lectures, several formal and informal discussions took place. The result was a wide and deep knowledge of the present research tendencies in the field. We wish to express our appreciation for the active contribution of all the par­ ticipants in the meeting. Our gratitude is due to the Ettore Majorana Centre in Erice, which offered its facilities and rewarding environment: its staff was certainly instrumental for the success of the meeting. Our gratitude is also due to Francisco Facchinei and Massimo Roma for the effort and time devoted as members of the Organising Committee. We are indebted to the Italian National Research Council, and in particular to the Group on Functional Analysis and its Applications and to the Committees on Engineering Sciences and on Information Sciences and Technolo­ gies for their financial support. Finally, we address our thanks to Kluwer Academic Publishers for having offered to publish this volume.

Generalized Lagrange multipliers: regularity and boundedness.- A primal-dual algorithm for minimizing a non-convex function subject to bound and linear equality constraints.- Minimal convexificators of a positively homogeneous function and a characterization of its convexity and concavity.- Optimal control problems and penalization.- A truncated Newton method for constrained optimization.- Fixed and virtual stability center methods for convex nonsmooth minimization.- Iterative methods for ill-conditioned linear systems from optimization.- An algorithm for solving nonlinear programs with noisy inequality constraints.- Generic existence, uniqueness and stability in optimization problems.- On a class of bilevel programs.- Separation methods for vector variational inequalities. Saddle point and gap function.- Functions with primal-dual gradient structure and U-Hessians.- Quadratic and multidimensional assignment problems.- A new merit function and an SQP method for non-strictly monotone variational inequalities.- A logarithmic barrier approach to Fischer function.- On an approach to optimization problems with a probabilistic cost and or constraints.- Semiderivative functions and reformulation methods for solving complementarity and variational inequality problems.- Global Lagrange multiplier rule and smooth exact penalty functions for equality constraints.- Structural methods in the solution of variational inequalities.- Extended nonlinear programming.- On the efficiency of splitting and projection methods for large strictly convex quadratic programs.- A comparison of rates of convergence of two inexact proximal point algorithms.- One way to construct a global search algorithm for d. c. minimization problems.- Error bounds and superlinear convergence analysis of some Newton-type methods in optimization.- A new derivative-free descent method for the nonlinear complementarity problem.