V. Jeyakumar & Alexander M. Rubinov 
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.

Cuprins

Surveys.- Linear Semi-infinite Optimization: Recent Advances.- Some Theoretical Aspects of Newton’s Method for Constrained Best Interpolation.- Optimization Methods in Direct and Inverse Scattering.- On Complexity of Stochastic Programming Problems.- Nonlinear Optimization in Modeling Environments.- Supervised Data Classification via Max-min Separability.- A Review of Applications of the Cutting Angle Methods.- Theory and Numerical Methods.- A Numerical Method for Concave Programming Problems.- Convexification and Monotone Optimization.- Generalized Lagrange Multipliers for Nonconvex Directionally Differentiable Programs.- Slice Convergence of Sums of Convex functions in Banach Spaces and Saddle Point Convergence.- Topical Functions and their Properties in a Class of Ordered Banach Spaces.- Applications.- Dynamical Systems Described by Relational Elasticities with Applications.- Impulsive Control of a Sequence of Rumour Processes.- Minimization of the Sum of Minima of Convex Functions and Its Application to Clustering.- Analysis of a Practical Control Policy for Water Storage in Two Connected Dams.