ABSTRACT
This chapter discusses several techniques to solve optimization problems. Optimization problems occur anywhere in chemical engineering, all to improve operation or design of process systems. Optimization models that have functions with discontinuities are harder to solve. Often, optimization is concerned with studying the derivatives of the functions and the derivative at a discontinuity does not exist. Also, discrete functions are discontinuous, e.g., pipe diameters that can be employed in the construction of a plant. Convexity of the functions will also tell how easily an optimization problem can be solved. In linear programming (LP), the objective function and the constraints are linear functions. A systematic method for finding the solution to an LP problem is the simplex method, which can be employed in an 8-step plan. In nonlinear programming (NLP), the objective function and/or the constraints can be nonlinear functions. The chapter approaches NLP problems with the Lagrange multiplier method, and Integer programming with the branch and bound algorithm.
