Related papers: Efficient Preconditioners for Interior Point Metho…
In this study, we focus on the numerical solution method for the optimal control problem with equilibrium constraints (OCPEC).It is extremely challenging to solve OCPEC owing to the absence of constraint regularity and strictly feasible…
The solution of matrices with $2\times 2$ block structure arises in numerous areas of computational mathematics, such as PDE discretizations based on mixed-finite element methods, constrained optimization problems, or the implicit or steady…
In this paper we theoretically show that interior-point methods based on self-concordant barriers possess favorable global complexity beyond their standard application area of convex optimization. To do that we propose first- and…
In this paper, we consider using Schur complements to design preconditioners for twofold and block tridiagonal saddle point problems. One type of the preconditioners are based on the nested (or recursive) Schur complement, the other is…
Computational methods are proposed for solving a convex quadratic program (QP). Active-set methods are defined for a particular primal and dual formulation of a QP with general equality constraints and simple lower bounds on the variables.…
We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling…
Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes…
The discretization of Cahn-Hilliard equation with obstacle potential leads to a block 2 by 2 non-linear system, where the p1, 1q block has a non-linear and non-smooth term. Recently a globally convergent Newton Schur method was proposed for…
If the Stokes equations are properly discretized, it is known that the Schur complement matrix is spectrally equivalent to the identity matrix. Moreover, in the case of simple geometries, it is often observed that most of its eigenvalues…
We study first-order methods with preconditioning for solving structured nonlinear convex optimization problems. We propose a new family of preconditioners generated by symmetric polynomials. They provide first-order optimization methods…
The interior-point method (IPM) has become the workhorse method for nonlinear programming. The performance of IPM is directly related to the linear solver employed to factorize the Karush--Kuhn--Tucker (KKT) system at each iteration of the…
This paper addresses black-box smooth optimization problems, where the objective and constraint functions are not explicitly known but can be queried. The main goal of this work is to generate a sequence of feasible points converging…
In this paper, we consider the composite optimization problem, where the objective function integrates a continuously differentiable loss function with a nonsmooth regularization term. Moreover, only the function values for the…
We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients $A$. We assume that the preconditioner is SPD on each step, and…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
We propose a k-space preconditioning formulation for accelerating the convergence of iterative Magnetic Resonance Imaging (MRI) reconstructions from non-uniformly sampled k-space data. Existing methods either use sampling density…
This paper is concerned with the least squares inverse eigenvalue problem of reconstructing a linear parameterized real symmetric matrix from the prescribed partial eigenvalues in the sense of least squares, which was originally proposed by…
In this paper, we propose an inertial accelerated primal-dual method for the linear equality constrained convex optimization problem. When the objective function has a ``nonsmooth + smooth'' composite structure, we further propose an…
A trajectory-following primal--dual interior-point method solves nonlinear optimization problems with inequality and equality constraints by approximately finding points satisfying perturbed Karush--Kuhn--Tucker optimality conditions for a…
We consider the iterative solution of regularized saddle-point systems. When the leading block is symmetric and positive semi-definite on an appropriate subspace, Dollar, Gould, Schilders, and Wathen (2006) describe how to apply the…