MATH 110B: OPTIMIZATION II

In this class, we study constrained optimization problems that include an objective function as well as constraints (or restrictions). We firstly deal with linear programs to minimize (or maximize) a linear objective function with linear constraints. There are various linear programs with equality and inequality constraints, but we consider the standard form of linear programs and learn the simplex methods to seek the optimal solution for the standard form. We also see dual problems of linear programs and find the relation between the original and dual problems. An interesting case of linear programs, the integer linear programming (ILP), is introduced, and some technical methods for ILP are presented. Furthermore, we deal with nonlinear constrained optimization problems having nonlinear objective functions or nonlinear constraints. In this case, the Lagrange condition and second-order conditions are applied to find local extrema.