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

Rachid Benouahboun; Abdelatif Mansouri

Displaying similar documents to “An interior point algorithm for convex quadratic programming with strict equilibrium constraints”

Newton and conjugate gradient for harmonic maps from the disc into the sphere

Morgan Pierre (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We compute numerically the minimizers of the Dirichlet energy $E (u) = \frac{1}{2} \int_{B^{2}} {| \nabla u |}^{2} d x$ among maps $u : B^{2} \to S^{2}$ from the unit disc into the unit sphere that satisfy a boundary condition and a degree condition. We use a Sobolev gradient algorithm for the minimization and we prove that its continuous version preserves the degree. For the discretization of the problem we use continuous finite elements. We propose an original mesh-refining strategy needed to preserve the degree with the discrete version...

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 $f : ℝ^{n \times m} \to ℝ$ , 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.

Generalized Characterization of the Convex Envelope of a Function

Fethi Kadhi (2010)

RAIRO - Operations Research

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We investigate the minima of functionals of the form $\int_{[a, b]} g (\dot{u} (s)) d s$ where is strictly convex. The admissible functions $u : [a, b] ⟶ ℝ$ are not necessarily convex and satisfy $u \leq f$ on , , , is a fixed function on . We show that the minimum is attained by $\bar{f}$ , the convex envelope of .

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 $\min_{u \in ϕ + W_{0}^{1, 1} (Ω)} \int_{Ω} [f (D u (x)) - u (x)] d x$ where $Ω \subseteq ℝ^{N}$ is a bounded convex open set, and the Borel function $f : ℝ^{N} \to [0, + \infty]$ 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.