Extended Frontiers in Optimization Techniques

Abstract

igin of the theory of geometrical optics. The problem of finding extreme values gained a special importance in the seventeenth century when it served as one of motivations in the invention of differential calculus. The soon after developed calculus of variations and the theory of stationary values lie in the foundation of the modern mathematical theory of optimization. The invention of the digital computer served as a powerful spur to the field of numerical optimization. During the World War II optimization algorithms were used to solve military logistics and operations problems. The military applications motivated the development of linear programming (LP), which studies optimization problems with linear objective function and constraints. In 1947 George Dantzig invented the simplex method for solving linear programs arising in U.S. Air Force operations. Linear programming has become one of the most popular and well studied optimization topics ever since. Although Dantzig is widely