Quasiconvex Programming and its Applications

Notion of convexity plays an important role in Economics and Engineering. The general equilibrium theory is based on convex programming. In classical economics, production and utility functions are assumed to be concave functions and as consequence, demand and cost functions are convex. The firm theory requires to solve the concave maximization problem while consumer theory considers utility maxmization problem. In recent years, generalized convex functions such as quasiconvex functions are found to be useful in Economics. In this book we consider two problems of maximizing and minimizing a quasiconvex function. Both problems belong to a class of global optimization and application of classical conditions has not been successful for solving these problems. Moreover, the Lagrangean method provides only a stationary point without guarantee of local optimality. For these reasons, global optimization appears to require new methods different from the standard nonlinear programming techniques. We derive new global optimality conditions for our problems and construct some algorithms the for convex case. We show applications of quasiconvex programming in economics and engineering.