although many methods exist for intensity modulated radiotherapy (imrt) fluence map optimization for crisp data, based on clinical practice, some of the involved parameters are fuzzy. in this paper, the best fluence maps for an imrt procedure were identifed as a solution of an optimization problem with a quadratic objective function, where the prescribed target dose vector was fuzzy. first, a d...

We propose a convex model for nonlocal image inpainting that fills in missing or damaged areas with different convex combinations of available image patches. The visual quality of inpainted solutions is much better when patches are copied instead of averaged, and we show how this can be achieved by adding a nonconvex sparsity promoting penalty. To promote sparsity of a variable that is constrai...

Based on work originating in the early 1970s, a number of recent global optimization algorithms have relied on replacing an original nonconvex nonlinear program by convex or linear relaxations. Such linear relaxations can be generated automatically through an automatic differentiation process. This process decomposes the objective and constraints (if any) into convex and nonconvex unary and bin...

This paper considers solving the unconstrained lq-norm (0 ≤ q < 1) regularized least squares (lq-LS) problem for recovering sparse signals in compressive sensing. We propose two highly efficient first-order algorithms via incorporating the proximity operator for nonconvex lq-norm functions into the fast iterative shrinkage/thresholding (FISTA) and the alternative direction method of multipliers...

We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numeric...

The continuation method is a popular heuristic in computer vision for nonconvex optimization. The idea is to start from a simplified problem and gradually deform it to the actual problem while tracking the solution. There are many choices for how to map the nonconvex objective to some convex task. One popular principle for such construction is Gaussian smoothing of the objective function. This ...

W propose a new robust optimization method for problems with objective functions that may be computed via numerical simulations and incorporate constraints that need to be feasible under perturbations. The proposed method iteratively moves along descent directions for the robust problem with nonconvex constraints and terminates at a robust local minimum. We generalize the algorithm further to m...