Search results for "Minimization problem"
showing 6 items of 6 documents
Branch and bound for the cutwidth minimization problem
2013
The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solu…
Some properties of [tr(Q2p)]12p with application to linear minimax estimation
1990
Abstract A nondifferentiable minimization problem is considered which occurs in linear minimax estimation. This problem is solved by replacing the nondifferentiable maximal eigenvalue of a real nonnegative definite matrix Q with [tr( Q 2 p )] 1/2 p . It is shown that any descent algorithm with inexact step-length rule can be used to obtain linear minimax estimators for the parameter vector of a parameter-restricted linear model.
Simultaneous zonation and calibration of pipe network parameters
2003
A procedure for simultaneously zoning and calibrating pipe network parameters is proposed and applied to the determination of pipe resistance coefficients. The methodology is aimed at grouping the parameters of all the pipes into a small number of zone parameters, constrained to keep the difference between the computed and the measured water heads below a given tolerance. It is shown that, in the case of nonlooped networks, the methodology leads to a linear minimization problem where the objective function is a measure of the heterogeneity of the estimated parameters. In the case of looped networks an iterative procedure, where the linear problem is coupled with a nonlinear problem having a…
A local chemical potential approach within the variable charge method formalism
2008
A new and computationally efficient implementation of the variable charge method of Streitz and Mintmire (1994 Phys. Rev. B 50 11996) is presented. In particular a local chemical potential approach that optimizes the charge on only those atoms expected to be ionic is developed. By doing so, the charge fluctuation problem experienced in regions far from any oxygen is solved, leading to a linear minimization problem of the electrostatic energy. In the dilute oxygen limit, such an approach can lead to at least an order of magnitude saving in computation.
Generalized Multitarget Linear Regression with Output Dependence Estimation
2019
Multitarget regression has recently received attention in the context of modern, large-scale problems in which finding good enough solutions in a timely manner is crucial. Different proposed alternatives use a combination of regularizers that lead to different ways of solving the problem. In this work, we introduce a general formulation with several regularizers. This leads to a biconvex minimization problem and we use an alternating procedure with accelerated proximal gradient steps to solve it. We show that our formulation is equivalent but more efficient than some previously proposed approaches. Moreover, we introduce two new variants. The experimental validation carried out, suggests th…
Existence of minimizers for eigenvalues of the Dirichlet-Laplacian with a drift
2015
Abstract This paper deals with the eigenvalue problem for the operator L = − Δ − x ⋅ ∇ with Dirichlet boundary conditions. We are interested in proving the existence of a set minimizing any eigenvalue λ k of L under a suitable measure constraint suggested by the structure of the operator. More precisely we prove that for any c > 0 and k ∈ N the following minimization problem min { λ k ( Ω ) : Ω quasi-open set , ∫ Ω e | x | 2 / 2 d x ≤ c } has a solution.