Applied optimization

Abstract

This manuscript provides a brief introduction to optimization problems. Optimization is essential in the studies of economy, engineering and other aspects of life. It covers basic calculus concepts to determine extrema of functions of single and several variables. Basic axioms of inner product spaces, metric, normed and topological spaces are discussed. Convex and concave functions equipped by examples and applications are given. Calculus of variation is discussed. Hamiltonian‘s ordinary difierential equations re discussed to enable us to solve optimization problem considering functionals