In optimization theory, the optimality conditions for interior points are usually much simpler than the optimality conditions for boundary points. In this chapter, we deal with the former, easier case. Boundary points appear more prominently in constrained optimization, when one tries to optimize a function, subject to several functional constraints. For this reason, the optimality conditions for boundary points are generally discussed in constrained optimization, whereas the optimality conditions for interior points are discussed in unconstrained optimization, regardless of whether the optimization problem at hand has constraints.
KeywordsSaddle Point Global Minimizer Symmetric Matrix Lower Semicontinuous Implicit Function Theorem
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