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Improving the predictive accuracy of a dynamics model is crucial to obtaining good control performance and safety from Model Predictive Controllers (MPC). One approach involves learning unmodelled (residual) dynamics, in addition to nominal…
The Continuous p-Dispersion Problem (CpDP) with boundary constraints asks for the placement of a fixed number of points in a compact subset of Euclidean space such that the minimum distance between any two points, as well as the points and…
Semidefinite programs (SDP) are one of the most versatile frameworks in numerical optimization, serving as generalizations of many conic programs and as relaxations of NP-hard combinatorial problems. Their main drawback is their…
Learning control policies for real-world robotic tasks often involve challenges such as multimodality, local discontinuities, and the need for computational efficiency. These challenges arise from the complexity of robotic environments,…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
In this paper, we aim to solve high dimensional convex quadratic programming (QP) problems with a large number of quadratic terms, linear equality and inequality constraints. In order to solve the targeted {\bf QP} problems to a desired…
In this paper, we present an optimization algorithm based on an alternating projection method to solve the large-scale security constraint optimal power flow (SCOPF) problem in power systems. The SCOPF is first partitioned into…
Coverage Path Planning (CPP) is vital in precision agriculture to improve efficiency and resource utilization. In irregular and dispersed plantations, traditional grid-based CPP often causes redundant coverage over non-vegetated areas,…
Quadratic programming (QP) is a well-studied fundamental NP-hard optimization problem which optimizes a quadratic objective over a set of linear constraints. In this paper, we reformulate QPs as a mixed-integer linear problem (MILP). This…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
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…
This paper presents a method to stabilize state and input constrained nonlinear systems using an offline optimization on variable triangulations of the set of admissible states. For control-affine systems, by choosing a continuous piecewise…
This article advocates the use of conformal prediction (CP) methods for Gaussian process (GP) interpolation to enhance the calibration of prediction intervals. We begin by illustrating that using a GP model with parameters selected by…
The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increasingly popular for incompressible flow problems but their…
Recent advances in 3D Gaussian Splatting (3DGS) have greatly improved 3D reconstruction. However, its substantial data size poses a significant challenge for transmission and storage. While many compression techniques have been proposed,…
In this paper, we present a novel solution for real-time, Non-Linear Model Predictive Control (NMPC) exploiting a time-mesh refinement strategy. The proposed controller formulates the Optimal Control Problem (OCP) in terms of flat outputs…
Combining recent moment and sparse semidefinite programming (SDP) relaxation techniques, we propose an approach to find smooth approximations for solutions of problems involving nonlinear differential equations. Given a system of nonlinear…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
This paper presents a novel approach to solve capacitated facility location problems (FLP) that encompass various resource allocation problems. FLPs are a class of NP-hard combinatorial optimization problems, involving optimal placement and…
The Computational Singular Perturbation (CSP) method of Lam and Goussis is an iterative method to reduce the dimensionality of systems of ordinary differential equations with multiple time scales. In [J. Nonlin. Sci., to appear], the…