Stochastic Gradient Descent in Non-Convex Landscapes What happens when optimization meets complexity? This project dives into the behavior of Stochastic Gradient Descent (SGD) when facing non-convex ...

This paper considers a class of distributed non-differentiable convex optimization problems, in which each local cost function is composed of a twice differentiable convex function and a lower ...

Min-max saddle point games appear in a wide range of applications in machine leaning and signal processing. Despite their wide applicability, theoretical studies are mostly limited to the special ...

This is the implementation of the differentiable optimization layer. This project features the ability to differentiate through a non-convex solver like scipy.minimize function. We mainly use ...

Abstract In this paper, we shall establish an inequality for differentiable co-ordinated convex functions on a rectangle from the plane. It is connected with the left side and right side of extended ...

Discover the proof that the average function of a trigonometrically ρ-convex function is also trigonometrically ρ-convex. Explore the existence of support curves and their implication on trigonometric ...

where ƒ: ℝ n → ℝ is a continuously differentiable function. In Section 2 we introduce the general framework for the study of algorithm performance and problem complexity and present a simple example.

This is illustrated in the above picture. I believe this is what Legendre did and then that what Fenchel did was to generalize this to non-differentiable functions. For non-differentiable functions, ...