perturbations

An Improved Method of Total Variation Superiorization Applied to Reconstruction in Proton Computed Tomography

  • Yair Censor
  • Paniz Karbasi
  • Keith E. Schubert
  • Reinhard W. Schulte
  • Blake Schultze
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , ,

    Previous work showed that total variation superiorization (TVS) improves reconstructed image quality in proton computed tomography (pCT). The structure of the TVS algorithm has evolved since then and this work investigated if this new algorithmic structure provides additional benefits to pCT image quality. Structural and parametric changes introduced to the original TVS algorithm included: (1) … Read more

    Zero-Convex Functions, Perturbation Resilience, and Subgradient Projections for Feasibility-Seeking Methods

  • Yair Censor
  • Daniel Reem
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , , , , , ,

    The convex feasibility problem (CFP) is at the core of the modeling of many problems in various areas of science. Subgradient projection methods are important tools for solving the CFP because they enable the use of subgradient calculations instead of orthogonal projections onto the individual sets of the problem. Working in a real Hilbert space, … Read more

    Prox-Regularity and Stability of the Proximal Mapping

  • Warren Hare
  • R. A. Poliquin
    • Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Robust Optimization Tags , , , ,

    Fundamental insights into the properties of a function come from the study of its Moreau envelopes and Proximal point mappings. In this paper we examine the stability of these two objects under several types of perturbations. In the simplest case, we consider tilt-perturbations, i.e. perturbations which correspond to adding a linear term to the objective … Read more

    A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs

  • Celso C. Ribeiro
  • Eduardo Uchoa
  • Renato F. Werneck
    • Categories Meta Heuristics, Telecommunications, VLSI layout Tags , , , ,

    We propose and describe a hybrid GRASP with weight perturbations and adaptive path-relinking heuristic (HGP+PR) for the Steiner problem in graphs. In this multi-start approach, the greedy randomized construction phase of a GRASP is replaced by the use of several construction heuristics with a weight perturbation strategy that combines intensification and diversification elements, as in … Read more