Motivation. mathematical review, matrix factorizations, sets and sequences, convex sets and functions, linear programming and simplex method, Weierstrass’ theorem, Karush Kuhn Tucker optimality conditions, algorithms, convergence, unconstrained optimization, Line search methods, method of multidimensional search, steepest descent methods, Newton’s method, modifications to Newton’s method, trust-region methods, conjugate gradient methods, quasi-Newton’s methods. constrained optimization, penalty, and barrier function methods augmented Lagrangian methods, polynomial-time algorithm for linear programming, successive linear programming, successive quadratic programming.