Exterior penalty function

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A penalty function in which the associated algorithm generates infeasible points, approaching feasibility in the limit towards a solution. An example is to maximize LaTeX: f(x) - u h(x)^2 over LaTeX: x \in X and let LaTeX: u \rightarrow \infty in order to approach the solution to

LaTeX: \max \{f(x): x \in X, \; h(x)=0\}.

If, during the penalty iterations, LaTeX: h(x^*)=0 for some finite LaTeX: u, then LaTeX: x^* solves the original mathematical program. Otherwise, the idea is that LaTeX: x^*(u) approaches the feasibility condition, LaTeX: h(x^*)=0, as LaTeX: u gets large (though this need not happen without assumptions on LaTeX: f and LaTeX: h).

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