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A constraint-reduced Mehrotra-Predictor-Corrector algorithm for convex quadratic programming is proposed. (At each iteration, such algorithms use only a subset of the inequality constraints in constructing the search direction, resulting in CPU savings.) The proposed algorithm makes use of a regularization scheme to cater to cases where the reduced constraint matrix is rank deficient. Global and local convergence properties are established under arbitrary working-set selection rules subject to satisfaction of a general condition. A modified active-set identification scheme that fulfills this condition is introduced. Numerical tests show great promise for the proposed algorithm, in particular for its active-set identification scheme. While the focus of the present paper is on dense systems, application of the main ideas to large sparse systems is briefly discussed.
A framework is proposed for solving general convex quadratic programs (CQPs) from an infeasible starting point by invoking an existing feasible-start algorithm tailored for inequality-constrained CQPs. The central tool is an exact penalty function sc
This paper presents a sparse solver based on the alternating direction method of multipliers algorithm for a linear model predictive control (MPC) formulation in which the terminal state is constrained to a given ellipsoid. The motivation behind this
We describe an active-set method for the minimization of an objective function $phi$ that is the sum of a smooth convex function and an $ell_1$-regularization term. A distinctive feature of the method is the way in which active-set identification and
We consider the minimization problem with the truncated quadratic regularization with gradient operator, which is a nonsmooth and nonconvex problem. We cooperated the classical preconditioned iterations for linear equations into the nonlinear differe
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including $ell^0$,