Related papers: Parallel KKT Solver in PIQP for Multistage Optimiz…
This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and…
In this article, a globally convergent sequential quadratic programming (SQP) method is developed for multi-objective optimization problems with inequality type constraints. A feasible descent direction is obtained using a linear…
In this paper, we study second-order necessary and sufficient optimality conditions of Karush--Kuhn--Tucker-type for locally optimal solutions in the sense of Pareto to a class of multi-objective optimal control problems with mixed…
This paper proposes efficient solutions for $k$-core decomposition with high parallelism. The problem of $k$-core decomposition is fundamental in graph analysis and has applications across various domains. However, existing algorithms face…
This paper introduces CKTSO (abbreviation of "circuit solver"), a novel sparse linear solver specially designed for the simulation program with integrated circuit emphasis (SPICE). CKTSO is a parallel solver and can be run on a multi-core,…
This system paper documents the technical foundations for the extension of the Topology ToolKit (TTK) to distributed-memory parallelism with the Message Passing Interface (MPI). While several recent papers introduced topology-based…
Scalable QR factorization algorithms for solving least squares and eigenvalue problems are critical given the increasing parallelism within modern machines. We introduce a more general parallelization of the CholeskyQR2 algorithm and show…
In this paper, we focus on efficient methods to solve discretized linear systems obtained from eddy current optimal control problems in an all-at-once approach. We construct a new low-rank matrix equation method based on a special splitting…
In this work, optimality conditions and classical results from duality theory are derived for continuous-time linear optimization problems with inequality constraints. The optimality conditions are given in the Karush-Kuhn-Tucker form. Weak…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
In this paper, we derive first and second-order optimality conditions of KKT type for locally optimal solutions to a class of multiobjective optimal control problems with endpoint constraint and mixed pointwise constraints. We give some…
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…
Multi-robot coordination often exhibits hierarchical structure, with some robots' decisions depending on the planned behaviors of others. While game theory provides a principled framework for such interactions, existing solvers struggle to…
We generalize the successive continuation paradigm introduced by Kern\'evez and Doedel [16] for locating locally optimal solutions of constrained optimization problems to the case of simultaneous equality and inequality constraints. The…
In this paper we present a parallelization strategy on distributed memory systems for the Fast Kinetic Scheme --- a semi-Lagrangian scheme developed in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] for solving kinetic equations. The…
The idea of embedding optimization problems into deep neural networks as optimization layers to encode constraints and inductive priors has taken hold in recent years. Most existing methods focus on implicitly differentiating…
Solving combinatorial optimization problems is a promising application area for quantum algorithms in real-world scenarios. In this work, we extend the "Quantum Tree Generator" (QTG), previously proposed for the 0-1 Knapsack Problem, to the…
This paper presents a practical global optimization algorithm for the K-center clustering problem, which aims to select K samples as the cluster centers to minimize the maximum within-cluster distance. This algorithm is based on a…
Many clustering applications in machine learning and data mining rely on solving metric-constrained optimization problems. These problems are characterized by $O(n^3)$ constraints that enforce triangle inequalities on distance variables…
We derive an extension of the sequential homotopy method that allows for the application of inexact solvers for the linear (double) saddle-point systems arising in the local semismooth Newton method for the homotopy subproblems. For the…