Continuous Optimization Current Trends and Modern Applications

Continuous optimization is the study of problems in which we wish to opti­ mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17*^ century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza­ tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re­ search in continuous optimization has produced a variety of theoretical devel­ opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin­ uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications.

Preface.- PART I. SURVEYS.- Linear Semi-infinite Optimization: Recent Advances (M.A. Goberna).- Some Theoretical Aspects of Newton's Method for Constrained Best Interpolation (H.-D. Qi).- Optimization Methods in Direct and Inverse Scattering (A.G. Ramm, S. Gutman).- On Complexity of Stochastic Programming Problems (A. Shapiro, A. Nemirovski).- Nonlinear Optimization in Modeling Environments: Software Implementations for Compilers, Spreadsheets, Modeling Languages, and Integrated Computing Systems (J.D. Pintér).- Supervised Data Classification via Max-min Separability (A.M. Bagirov, J. Ugon).- A Review of Applications of the Cutting Angle Methods (G. Beliakov).- PART II. THEORY AND NUMERICAL METHODS.- A Numerical Method for Concave Programming Problems (A. Chinchuluun, E. Rentsen, P.M. Pardalos).- Convexification and Monotone Optimization (X. Sun, J. Li, D. Li).- Generalized Lagrange Multipliers for Nonconvex Directionally Differentiable Programs (N. Dinh, G.M. Lee, L.A. Tuan).- Slice Convergence of Sums of Conves Functions in Banach Spaces and Saddle Point Convergence (R. Wenczel, A. Eberhard).- Topical Functions and Their Properties in a Class of Ordered Banach Spaces (H. Mohebi).- PART III. APPLICATIONS.- Dynamical Systems Described by Relational Elasticities with Applications (M. Mammadov, A. Rubinov, J. Yearwood).- Impulsive Control of a Sequence of Rumour Processes (C. Pearce, Y. Kaya, S. Belen).- Minimization of the Sum of Minima of Conves Functions and Its Application to Clustering (A. Rubinov, N. Soukhorokova, J. Ugon).- Analysis of a Practical Control Policy for Water Storage in Two Connected Dams (P. Howlett, J. Piantadosi, C. Pearce).