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Difference between convex and non-convex cost function; what does it mean when a cost function is non-convex?

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Taken from Cho-Jui Hsieh, UCLA

A convex function is one where a line drawn between any two points on the graph lies on or above the graph. It has one minimum.

A non-convex function is one where a line drawn between any two points on the graph may intersect other points on the graph. It characterized as “wavy”.

When a cost function is non-convex, it means that there’s a likelihood that the function may find local minima instead of the global minimum, which is typically undesired in machine learning models from an optimization perspective.

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