Related papers: A Massively Parallel Interior-Point Method for Arr…
Quantum Interior Point Methods (QIPMs) have been attracting significant interests recently due to their potential of solving optimization problems substantially faster than state-of-the-art conventional algorithms. In general, QIPMs use…
We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…
Bilevel optimization has been widely used in decision-making process. However, there still lacks an efficient algorithm to determine an optimal solution of a bilevel optimization problem, especially for a large-size problem. To bridge the…
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…
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it…
We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that…
Solving optimization problems with transient PDE-constraints is computationally costly due to the number of nonlinear iterations and the cost of solving large-scale KKT matrices. These matrices scale with the size of the spatial…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…
In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of…
Quantum linear system algorithms (QLSAs) have the potential to speed up algorithms that rely on solving linear systems. Interior Point Methods (IPMs) yield a fundamental family of polynomial-time algorithms for solving optimization…
As renewable energy integration, sector coupling, and spatiotemporal detail increase, energy system optimization models grow in size and complexity, often pushing solvers to their performance limits. This systematic review explores…
Nonlinear optimization problems are found at the heart of real-time operations of critical infrastructures. These problems are computationally challenging because they embed complex physical models that exhibit space-time dynamics. We…
There are variety of computational algorithms need sequential sweeping; sweeping based on specific order; on a structured grid, e.g., preconditioning (smoothing) by SOR or ILU methods and solution of eikonal equation by fast sweeping…
Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a sparse structure of input SDP by…
This paper pushes further the intrinsic capabilities of the GFEM$^{gl}$ global-local approach introduced initially in [1]. We develop a distributed computing approach using MPI (Message Passing Interface) both for the global and local…
Interpolative and CUR decompositions involve "natural bases" of row and column subsets, or skeletons, of a given matrix that approximately span its row and column spaces. These low-rank decompositions preserve properties such as sparsity or…
Interior-point methods for linear programming problems require the repeated solution of a linear system of equations. Solving these linear systems is non-trivial due to the severe ill-conditioning of the matrices towards convergence. This…
An interior-point algorithm framework is proposed, analyzed, and tested for solving nonlinearly constrained continuous optimization problems. The main setting of interest is when the objective and constraint functions may be nonlinear…
Many problems of interest for cyber-physical network systems can be formulated as Mixed-Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithmic framework to solve…
We propose a localized divide and conquer algorithm for inverse factorization $S^{-1} = ZZ^*$ of Hermitian positive definite matrices $S$ with localized structure, e.g. exponential decay with respect to some given distance function on the…