Abstract
In this chapter, various optimizations techniques are discussed, and through these techniques, different multivariable constrained nonlinear optimization problems can be investigated. First, classical methods are described to handle the same. In this context, both the inequality and mixed (equality and inequality) type constraints are considered, and the formulated optimization problems are demonstrated. Then several numerical techniques are taken to manage multivariable constrained nonlinear optimization problems. Furthermore, different types of penalty methods, viz., interior and exterior penalty methods are employed to obtain the optimal solution for multivariable constrained nonlinear optimization problems. Finally, algorithms are given for easy implementation of the mentioned methods.
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