Displaying similar documents to “The Lazy Travelling Salesman Problem in ℝ 2 ”

Linear convergence in the approximation of rank-one convex envelopes

Sören Bartels (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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A linearly convergent iterative algorithm that approximates the rank-1 convex envelope  f r c of a given function f : ℝ n × m → ℝ , the largest function below which is convex along all rank-1 lines, is established. The proposed algorithm is a modified version of an approximation scheme due to Dolzmann and Walkington.

An interior point algorithm for convex quadratic programming with strict equilibrium constraints

Rachid Benouahboun, Abdelatif Mansouri (2010)

RAIRO - Operations Research

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We describe an interior point algorithm for convex quadratic problem with a strict complementarity constraints. We show that under some assumptions the approach requires a total of O ( n L ) number of iterations, where is the input size of the problem. The algorithm generates a sequence of problems, each of which is approximately solved by Newton's method.

Geometric constraints on the domain for a class of minimum problems

Graziano Crasta, Annalisa Malusa (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider minimization problems of the form min u ∈ ϕ + W 0 1 , 1 ( Ω ) ∫ Ω [ f ( D u ( x ) ) - u ( x ) ] d x where Ω ⊆ ℝ N is a bounded convex open set, and the Borel function f : ℝ N → [ 0 , + ∞ ] is assumed to be neither convex nor coercive. Under suitable assumptions involving the geometry of and the zero level set of , we prove that the viscosity solution of a related Hamilton–Jacobi equation provides a minimizer for the integral functional.