Florentin Goyens

Complexity of quadratic penalty methods with adaptive accuracy under a PL condition for the constraints

  • Florentin Goyens
  • Geovani Nunes Grapiglia
    • Categories Constrained Nonlinear Optimization Tags , , ,

    We study the quadratic penalty method (QPM) for smooth nonconvex optimization problems with equality constraints. Assuming the constraint violation satisfies the PL condition near the feasible set, we derive sharper worst-case complexity bounds for obtaining approximate first-order KKT points. When the objective and constraints are twice continuously differentiable, we show that QPM equipped with a … Read more

    Riemannian trust-region methods for strict saddle functions with complexity guarantees

  • Florentin Goyens
  • ClĂ©ment W. Royer
    • Categories Nonlinear Optimization Tags , , ,

    The difficulty of minimizing a nonconvex function is in part explained by the presence of saddle points. This slows down optimization algorithms and impacts worst-case complexity guarantees. However, many nonconvex problems of interest possess a favorable structure for optimization, in the sense that saddle points can be escaped efficiently by appropriate algorithms. This strict saddle … Read more

    Nonlinear matrix recovery using optimization on the Grassmann manifold

  • Coralia Cartis
  • Armin Eftekhari
  • Florentin Goyens
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , ,

    We investigate the problem of recovering a partially observed high-rank matrix whose columns obey a nonlinear structure such as a union of subspaces, an algebraic variety or grouped in clusters. The recovery problem is formulated as the rank minimization of a nonlinear feature map applied to the original matrix, which is then further approximated by … Read more