fenchel conjugate

Cutting-plane algorithm for sparse estimation of the Cox proportional-hazards model

  • Hiroki Saishu
  • Kota Kudo
  • Yuichi Takano
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Statistics Tags , , , , ,

    Survival analysis is a family of statistical methods for analyzing event occurrence times. In this paper, we address the mixed-integer optimization approach to sparse estimation of the Cox proportional-hazards model for survival analysis. Specifically, we propose a high-performance cutting-plane algorithm based on reformulation of bilevel optimization for sparse estimation. This algorithm solves the upper-level problem … Read more

    Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

  • Radu Ioan Bot
  • Ernö Robert Csetnek
  • Nimit Nimana
    • Categories Complementarity and Variational Inequalities, Convex and Nonsmooth Optimization Tags , , ,

    We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take … Read more

    Forward-Backward and Tseng’s Type Penalty Schemes for Monotone Inclusion Problems

  • Radu Ioan Bot
  • Ernö Robert Csetnek
    • Categories Convex Optimization Tags , , , , , , , ,

    We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We propose a forward-backward penalty algorithm for solving this problem which extends the one proposed by H. Attouch, … Read more

    The kernel average for two convex functions and its application to the extension and representation of monotone operators

  • Heinz Bauschke
  • Xianfu Wang
    • Categories Convex Optimization Tags , , , , , , , , ,

    We provide and analyze a based average for two convex functions, based on a kernel function. It covers several known averages such as the arithmetic average, epigraphical average, and the proximal average. When applied to the Fitzpatrick function and the conjugate of Fitzpatrick function associated with a monotone operator, our average produces an autoconjugate (also … Read more