(BQ) Part 2 book "Engineering optimization theory and practice" has contents: Nonlinear programming III-Constrained optimization techniques, geometric programming, dynamic programming, dynamic programming, stochastic programming, stochastic programming, practical aspects of optimization,.and other contents. | 7 Nonlinear Programming III: Constrained Optimization Techniques INTRODUCTION This chapter deals with techniques that are applicable to the solution of the constrained optimization problem: Find X which minimizes f (X) subject to gj (X) ≤ 0, j = 1, 2, . . . , m hk (X) = 0, k = 1, 2, . . . , p () There are many techniques available for the solution of a constrained nonlinear programming problem. All the methods can be classified into two broad categories: direct methods and indirect methods, as shown in Table . In the direct methods, the constraints are handled in an explicit manner, whereas in most of the indirect methods, the constrained problem is solved as a sequence of unconstrained minimization problems. We discuss in this chapter all the methods indicated in Table . CHARACTERISTICS OF A CONSTRAINED PROBLEM In the presence of constraints, an optimization problem may have the following features [, ]: 1. The constraints may have no effect on the optimum point; that is, the constrained minimum is the same as the unconstrained minimum as shown in Fig. . In this case the minimum point X∗ can be found by making use of the necessary and sufficient conditions ∇f |X∗ = 0 JX∗ = 380 () ∂ 2f ∂xi ∂xj Engineering Optimization: Theory and Practice, Fourth Edition Copyright © 2009 by John Wiley & Sons, Inc. = positive definite X∗ Singiresu S. Rao () Characteristics of a Constrained Problem Table 381 Constrained Optimization Techniques Direct methods Random search methods Heuristic search methods Complex method Objective and constraint approximation methods Sequential linear programming method Sequential quadratic programming method Methods of feasible directions Zoutendijk’s method Rosen’s gradient projection method Generalized reduced gradient method Indirect methods Transformation of variables technique Sequential unconstrained minimization techniques Interior penalty function method Exterior penalty function .
