This paper addresses a constrained two-dimensional (2D) non-guillotine cutting problem, where a fixed set of small rectangles has to be cut from a larger stock rectangle so as to maximize the value of the rectangles cut. The algorithm we propose hybridizes a novel placement procedure with a genetic algorithm based on random keys. We propose … Read more
We present computational approaches for optimizing beam angles and fluence maps in Intensity Modulated Radiation Therapy (IMRT) planning. We assume that the number of angles to be used for the treatment is given by the treatment planner. A mixed integer programming (MIP) model and a linear programming (LP) model are used to find an optimal … Read more
We consider the effectiveness of a lookahead branching method for the selection of branching variable in branch-and-bound method for mixed integer programming. Specifically, we ask the following question: by taking into account the impact of the current branching decision on the bounds of the child nodes two levels deeper than the current node, can better … Read more
In this work we present a family of variable metric interior proximal methods for solving optimization problems under nonnegativity constraints. We define two algorithms, in the inexact and exact forms. The kernels are metrics generated by diagonal matrices in each iteration and the regularization parameters are conveniently chosen to force the iterates to be interior … Read more
We study the second-order feasibility cone F = { y : \| My \| \le g^Ty } for given data (M,g). We construct a new representation for this cone and its dual based on the spectral decomposition of the matrix M^TM – gg^T. This representation is used to efficiently solve the problem of projecting an … Read more
The classical perceptron algorithm is an elementary row-action/relaxation algorithm for solving a homogeneous linear inequality system Ax > 0. A natural condition measure associated with this algorithm is the Euclidean width t of the cone of feasible solutions, and the iteration complexity of the perceptron algorithm is bounded by 1/t^2, see Rosenblatt 1962. Dunagan and … Read more
We consider the question of global convergence of iterative methods for nonlinear programming problems. Traditionally, penalty functions have been used to enforce global convergence. In this paper we review a recent alternative, so-called filter methods. Instead of combing the objective and constraint violation into a single function, filter methods view nonlinear optimization as a biobjective … Read more
In the paper, we consider the chance constrained version $$ \Prob\{A_0[x]+\sum_{i=1}^d\zeta_i A_i[x]\succeq0\}\geq1-\epsilon, $$ of an affinely perturbed Linear Matrix Inequality constraint; here $A_i[x]$ are symmetric matrices affinely depending on the decision vector $x$, and $\zeta_1,…,\zeta_d$ are independent of each other random perturbations with light tail distributions (e.g., bounded or Gaussian). Constraints of this type, playing … Read more
The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity, metric regularity along a subspace, strong metric regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version … Read more
We consider the problem of identifying multiple outliers in linear regression models. In robust regression the unusual observations should be removed from the sample in order to obtain better fitting for the rest of the observations. Based on the LTS estimate, we propose a penalized trimmed square estimator PTS, where penalty costs for discarding outliers … Read more