Related papers: Simultaneous diagonalization via congruence of $m$…
Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic,…
Quadratically constrained quadratic programming (QCQP) has long been recognized as a computationally challenging problem, particularly in large-scale or high-dimensional settings where solving it directly becomes intractable. The complexity…
We introduce a verification framework to exactly verify the worst-case performance of sequential convex programming (SCP) algorithms for parametric non-convex optimization. The verification problem is formulated as an optimization problem…
In this work, based on the ideas of alternating direction method with multipliers (ADMM) and sequential quadratic programming (SQP), as well as Armijo line search technology, monotone splitting SQP algorithms for two-block nonconvex…
In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality…
Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple…
The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive…
This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing…
We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of two matrices and the symplectic orthogonal transformation of…
In this paper, we propose two algorithms for nonlinear semi-infinite semi-definite programs with infinitely many convex inequality constraints, called SISDP for short. A straightforward approach to the SISDP is to use classical methods for…
We consider the problem of finding the optimal diagonal preconditioner for a positive definite matrix. Although this problem has been shown to be solvable and various methods have been proposed, none of the existing approaches are scalable…
Identifying the connected components of a graph, apart from being a fundamental problem with countless applications, is a key primitive for many other algorithms. In this paper, we consider this problem in parallel settings. Particularly,…
We survey recent progress on efficient algorithms for approximately diagonalizing a square complex matrix in the models of rational (variable precision) and finite (floating point) arithmetic. This question has been studied across several…
The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…
We present the first parallel algorithm for solving systems of linear equations in symmetric, diagonally dominant (SDD) matrices that runs in polylogarithmic time and nearly-linear work. The heart of our algorithm is a construction of a…
The {\sc $c$-Balanced Separator} problem is a graph-partitioning problem in which given a graph $G$, one aims to find a cut of minimum size such that both the sides of the cut have at least $cn$ vertices. In this paper, we present new…
Asynchronous methods for solving systems of linear equations have been researched since Chazan and Miranker's pioneering 1969 paper on chaotic relaxation. The underlying idea of asynchronous methods is to avoid processor idle time by…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
In dual decomposition, the dual to an optimization problem with a specific structure is solved in distributed fashion using (sub)gradient and recently also fast gradient methods. The traditional dual decomposition suffers from two main…
We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the one hand, this offers a simple description of SDP. On the…