quasar-convexity

Boosted Stochastic Frank-Wolfe for Constrained Nonconvex Optimization

  • navil_26
  • Abbas Khademi
  • Antonio Silveti-Falls
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , ,

    The boosted Frank-Wolfe algorithm accelerates the classical Frank-Wolfe algorithm by better aligning the update direction with the negative gradient. Its analysis, however, has been limited to deterministic convex problems, with step sizes that require either line search or knowledge of the Lipschitz constant of the gradient. We develop a novel step size strategy that does … Read more

    The Convexity Zoo: A Taxonomy of Function Classes in Optimization

  • Abbas Khademi
    • 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