Approximating Optima of Nonconvex Functions

K Lakshmanan

Keywords: Computablity of Approximate Optima, Non-convex functions

TL;DR: studies the computability of approximating optima for non-convex functions

Abstract: We study the computability of approximating optima of non-convex functions. We give a simple proof to show that the problem of finding the optimal value (and optimal point) or its approximation is not even computable in the oracle setting. We also give a property a function has to satisfy if its global optima can be approximated. Next we give an example of such a global property we call basin of attraction. Then we give a simple algorithm which converges to the global optima when this is known. Finally, we give some numerical results.

Primary Area: optimization

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Submission Number: 3476