Related papers: A Preconditioned Iterative Interior Point Approach…
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…
In this paper, we examine the problem of partial inference in the context of structured prediction. Using a generative model approach, we consider the task of maximizing a score function with unary and pairwise potentials in the space of…
This paper introduces inexact versions of several block-splitting preconditioners for solving the three-by-three block linear systems arising from a special class of indefinite least squares problems. We first establish the convergence…
It was recently demonstrated that the boundary element method based on the Burton-Miller formulation (BM-BEM), widely used for solving exterior problems, can be adapted to solve transmission problems efficiently. This approach utilises…
In this paper, we consider a nonlinear semi-infinite program that minimizes a function including a log-determinant (logdet) function over positive definite matrix constraints and infinitely many convex inequality constraints, called SIPLOG…
Numerical simulation of fracture contact poromechanics is essential for various applications, including CO2 sequestration, geothermal energy production and underground gas storage. Modeling this problem accurately presents significant…
We present a preconditioner based on spectral projection that is combined with a deflated Krylov subspace method for solving ill conditioned linear systems of equations. Our results show that the proposed algorithm requires many fewer…
We consider regularized cutting-plane methods to minimize a convex function that is the sum of a large number of component functions. One important example is the dual problem obtained from Lagrangian relaxation on a decomposable problem.…
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
A new iteration bound for the preconditioned conjugate gradient (PCG) method is presented that more accurately captures convergence for systems with clustered eigenspectra, where the classical condition number-based bound is too…
In this research, to solve the large indefinite least squares problem, we firstly transform its normal equation into a sparse block three-by-three linear systems, then use GMRES method with an accelerated preconditioner to solve it. The…
We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible…
We develop a spatial branch-and-cut approach for nonconvex Quadratically Constrained Quadratic Programs with bounded complex variables (CQCQP). Linear valid inequalities are added at each node of the search tree to strengthen semidefinite…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…
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…
We present a stationary iteration method, namely Alternating Symmetric positive definite and Scaled symmetric positive semidefinite Splitting (ASSS), for solving the system of linear equations obtained by using finite element discretization…
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as…
Particle swarm optimization is used in several combinatorial optimization problems. In this work, particle swarms are used to solve quadratic programming problems with quadratic constraints. The approach of particle swarms is an example for…
In this work, we develop proximal preconditioned gradient methods with a focus on spectral gradient methods providing a proximal extension to the Muon and Scion optimizers. We introduce a family of stochastic algorithms that can handle a…