Fundamentals of constrained optimization
In unconstrained optimization the independent variables x are allowed to take any finite value. For many problems this kind of approach is not useful because it is known a priori from properties of the system under study that certain points are unacceptable as solutions. Restrictions on the value of x are formulated as constraints and constrained optimization is the study of methods for solving this type of problem. The present chapter deals with the characterisation of constrained minima. Since this is a subject of considerably greater complexity than the unconstrained analogue, a completely general and rigorous treatment is beyond the scope of this book. Simplifying assumptions, of relatively slight practical significance, are introduced now and then, and difficult mathematics is avoided by appeal to the reader’s intuition where this is felt appropriate.
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