structured nonconvexity

Weakly Quasar-Convex Optimization

Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Nonlinear Optimization Tags , , , ,

This paper introduces the class of weakly quasar-convex functions, a notion that simultaneously generalizes weak convexity (and hence convexity) and quasar-convexity. We establish the theoretical foundation for this new class by developing its basic calculus, deriving characterizations, and systematically investigating its closure and structural properties. Building on these tools, we analyze the proximal point algorithm … Read more

The Convexity Zoo: A Taxonomy of Function Classes in Optimization

Categories Generalized Convexity/Monoticity, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

The tractability of optimization problems depends critically on structural properties of the objective function. Convexity guarantees global optimality of local solutions and enables polynomial-time algorithms under mild assumptions, but many problems arising in modern applications—particularly in machine learning—are inherently nonconvex. Remarkably, a large class of such problems remains amenable to efficient optimization due to additional … Read more