Advanced Optimization for Process Systems Engineering

This chapter first introduces basic concepts in nonlinear optimization, especially feasible regions and convexity conditions. Sufficient conditions are provided for both convex regions and convex functions. Next, optimality conditions are presented for unconstrained optimization problems (stationary conditions), and constrained problems with equality constraints (stationary condition of Lagrange function) and with inequality constraints (Fritz-John Theorem).The chapter concludes with nonlinear optimization with equality and equalityconstraints that lead to the Karush–Kuhn–Tucker conditions. Finally, an active set strategy is introduced for the solution of small nonlinear programming problems, and is illustrated with a small example.