We consider a time-optimal problem for the Reeds and Shepp model describing a moving point on a plane, with a free final direction of velocity. Using Pontryagin Maximum Principle, we obtain all types of extremals and, analysing them and discarding nonoptimal ones, construct the optimal synthesis. Article Download View Optimal synthesis in the Reeds and … Read more
This paper presents a new two-phase solution approach to the beam angle and fluence map optimization problem in Intensity Modulated Radiation Therapy (IMRT) planning. We introduce Branch-and-Prune (B&P) to generate a robust feasible solution in the first phase. A local neighborhood search algorithm is developed to find a local optimal solution from the Phase I … Read more
We present an approach to estimate adjoint sensitivities of economic metrics of relevance in the power grid with respect to physical weather variables using numerical weather prediction models. We demonstrate that this capability can significantly enhance planning and operations. We illustrate the method using a large-scale computational study where we compute sensitivities of the regional … Read more
In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is di fferentiable and satisfi es the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove … Read more
We propose a proximal point algorithm to solve LAROS problem, that is the problem of finding a “large approximately rank-one submatrix”. This LAROS problem is used to sequentially extract features in data. We also develop a new stopping criterion for the proximal point algorithm, which is based on the duality conditions of \eps-optimal solutions of … Read more
In this work we propose solving huge-scale instances of the truss topology design problem with coordinate descent methods. We develop four efficient codes: serial and parallel implementations of randomized and greedy rules for the selection of the variable (potential bar) to be updated in the next iteration. Both serial methods enjoy an O(n/k) iteration complexity … Read more
In this paper we present an iterative algorithm for the solution of regularization problems arising in inverse image processing. The regularization function to be minimized is constituted by two terms, a data fit function and a regularization function, weighted by a regularization parameter. The proposed algorithm solves the minimization problem and estimates the regularization parameter … Read more
Iterative methods that calculate their steps from approximate subgradient directions have proved to be useful for stochastic learning problems over large and streaming data sets. When the objective consists of a loss function plus a nonsmooth regularization term, the solution often lies on a low-dimensional manifold of parameter space along which the regularizer is smooth. … Read more
The rank function $\rank(\cdot)$ is neither continuous nor convex which brings much difficulty to the solution of rank minimization problems. In this paper, we provide a unified framework to construct the approximation functions of $\rank(\cdot)$, and study their favorable properties. Particularly, with two families of approximation functions, we propose a convex relaxation method for the … Read more
The stable principal component pursuit (SPCP) problem is a non-smooth convex optimization problem, the solution of which has been shown both in theory and in practice to enable one to recover the low rank and sparse components of a matrix whose elements have been corrupted by Gaussian noise. In this paper, we first show how … Read more