Related papers: OSQP: An Operator Splitting Solver for Quadratic P…
This paper proposes and analyzes a new operator splitting method for stochastic Maxwell equations driven by additive noise, which not only decomposes the original multi-dimensional system into some local one-dimensional subsystems, but also…
This paper introduces an efficient algorithm for computing the general oscillatory matrix functions. These computations are crucial for solving second-order semi-linear initial value problems. The method is exploited using the scaling and…
We introduce an algorithmic framework for performing QR factorization with column pivoting (QRCP) on general matrices. The framework enables the design of practical QRCP algorithms through user-controlled choices for the core subroutines.…
The paper suggests a preconditioning type method for fast solving of elliptic equations with oscillating quasiperiodic coefficients $A_\epsilon$ specified by the small parameter $\epsilon>0$. We use an iteration method generated by an…
This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…
Conic programs arise broadly in physics, quantum information, machine learning, and engineering, many of which are defined over sparse graphs. Although such problems can be solved in polynomial time using classical interior-point solvers,…
Outer approximation methods have long been employed to tackle a variety of optimization problems, including linear programming, in the 1960s, and continue to be effective for solving variational inequalities, general convex problems, as…
We propose the novel p-branch-and-bound method for solving two-stage stochastic programming problems whose deterministic equivalents are represented by non-convex mixed-integer quadratically constrained quadratic programming (MIQCQP)…
Feasible path algorithms have been widely used for process optimisation due to its good convergence. The sequential quadratic programming (SQP) algorithm is usually used to drive the feasible path algorithms towards optimality. However,…
This paper addresses the problem of solving nonlinear systems in the context of symmetric quantum signal processing (QSP), a powerful technique for implementing matrix functions on quantum computers. Symmetric QSP focuses on representing…
Convex separable quadratic optimization problems occur in many practical applications. In this paper, based on an iterative resolution scheme of the KKT system, we develop an efficient method for solving a quadratic programming problem with…
Nonlinear model predictive control~(NMPC) generally requires the solution of a non-convex optimization problem at each sampling instant under strict timing constraints, based on a set of differential equations that can often be stiff and/or…
A numerical framework based on network partition and operator splitting is developed to solve nonlinear differential equations of large-scale dynamic processes encountered in physics, chemistry and biology. Under the assumption that those…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…
We introduce the MATLAB-based software QuITO (Quasi-Interpolation based Trajectory Optimization) to numerically solve a wide class of constrained nonlinear optimal control problems (OCP). The solver is based on the QuITO (the same…
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…
In this paper, we propose a parallel shooting algorithm for solving nonlinear model predictive control problems using sequential quadratic programming. This algorithm is built on a two-phase approach where we first test and assess…
A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We…
Operator splitting is a popular divide-and-conquer strategy for solving differential equations. Typically, the right-hand side of the differential equation is split into a number of parts that are then integrated separately. Many methods…