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To clarify, "global" in this context refers to global convergence (as in, it won't diverge no matter the starting point), not global optima. They assume a conve
by MauranKilom 5y ago
To clarify, "global" in this context refers to global convergence (as in, it won't diverge no matter the starting point), not global optima. They assume a convex function, i.e. only a single minimum. The paper is unrelated to avoiding local minima.
- abetusk 5y agoSo isn't the magic here convexity? Convexity is such a huge constraint that I would guess convergence would be hard to avoid.
- jleahy 5y agoTell that to Newton’s method, which can fail to converge for convex functions.
- kergonath 5y agoThere is no way of ensuring that you have found a global minimum if the function is not convex, or if you don’t make equivalent assumptions, in the general case (if the domain of the function is continuous, and/or infinite). If you don’t make assumptions, you would need to consider every single point of the domain, and there is an infinite number of them. The job gets easier the more assumptions you make about the continuous, differentiable, and monotonous character of the function.