An infeasible Predictor-Corrector Interior Point Method Applied to Image Denoising

Projet PROMATHImage recovery problems can be solved using optimization techniques. In this case, they often lead to the resolution of either a large scale quadratic program, or, equivalently, to a nondifferentiable minimization problem. Interior point methods are widely known for their efficiency in linear programming. Lately, they have been extended with success to the resolution of linear complementary problems, (LCP), which include convex quadratic programming. We present an infeasible predictor-corrector interior point method, in the general framework of monotone (LCP). The algorithm has polynomial complexity. We also prove it converges globally, with asymptotic quadratic rate. We apply this method to the denoising of images. In the implementation we take advantage of the underlying structure of the problem, specially its sparsity. We obtain good performances, that we assess by comparing the method with a variable-metric proximal bundle algorithm applied to the resolution of the equivalent nonsmooth problem

An interior-point and decomposition approach to multiple stage stochastic programming

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An Improved Predictor-Corrector Interior-Point Algorithm for Linear Complementarity Problems with -Iteration Complexity

This paper proposes an improved predictor-corrector interior-point algorithm for the linear complementarity problem (LCP) based on the Mizuno-Todd-Ye algorithm. The modified corrector steps in our algorithm cannot only draw the iteration point back to a narrower neighborhood of the center path but also reduce the duality gap. It implies that the improved algorithm can converge faster than the MTY algorithm. The iteration complexity of the improved algorithm is proved to obtain √() which is similar to the classical Mizuno-Todd-Ye algorithm. Finally, the numerical experiments show that our algorithm improved the performance of the classical MTY algorithm