Related papers: Active-set prediction in quadratic programming usi…
Auxiliary variables are often used to model a convex piecewise linear function in the framework of linear optimization. This work shows that such variables yield a block diagonal plus low rank structure in the reduced KKT system of the dual…
This paper presents a new approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at…
In this paper, we present a control synthesis framework for a general class of nonlinear, control-affine systems under spatiotemporal and input constraints. First, we study the problem of fixed-time convergence in the presence of input…
This work investigates the challenge of ensuring safety guarantees in the presence of uncontrollable agents, whose behaviors are stochastic and depend on both their own and the system's states. We present a neural model predictive control…
A robust model predictive control (MPC) method is presented for linear, time-invariant systems affected by bounded additive disturbances. The main contribution is the offline design of a disturbance-affine feedback gain whereby the…
We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
We provide a condition-based analysis of two interior-point methods for unconstrained geometric programs, a class of convex programs that arise naturally in applications including matrix scaling, matrix balancing, and entropy maximization.…
This paper presents a computationally-efficient method for evaluating the feasibility of Quadratic Programs (QPs) for online constrained control. Based on the duality principle, we first show that the feasibility of a QP can be determined…
In this paper we will discuss two variants of an inexact feasible interior point algorithm for convex quadratic programming. We will consider two different neighbourhoods: a (small) one induced by the use of the Euclidean norm which yields…
Quadratic invariance is a condition which has been shown to allow for optimal decentralized control problems to be cast as convex optimization problems. The condition relates the constraints that the decentralization imposes on the…
Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its…
We study unconstrained and constrained linear quadratic problems and investigate the suboptimality of the model predictive control (MPC) method applied to such problems. Considering MPC as an approximate scheme for solving the related fixed…
Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…
In the vicinity of a solution of a nonlinear programming problem at which both strict complementarity and linear independence of the active constraints may fail to hold, we describe a technique for distinguishing weakly active from strongly…
This paper presents PIQP, a high-performance toolkit for solving generic sparse quadratic programs (QP). Combining an infeasible Interior Point Method (IPM) with the Proximal Method of Multipliers (PMM), the algorithm can handle…
A challenging category of robotics problems arises when sensing incurs substantial costs. This paper examines settings in which a robot wishes to limit its observations of state, for instance, motivated by specific considerations of energy…
Small-scale Mixed-Integer Quadratic Programming (MIQP) problems often arise in embedded control and estimation applications. Driven by the need for algorithmic simplicity to target computing platforms with limited memory and computing…
Iteration limited model predictive control (MPC) can stabilize a feedback control system under sufficient conditions; this work explores combining a low iteration limit MPC with a high iteration limit MPC for mixed-integer quadratic…
In this letter, an accelerated quadratic programming (QP) algorithm is proposed based on the proximal gradient method. The algorithm can achieve convergence rate $O(1/p^{\alpha})$, where $p$ is the iteration number and $\alpha$ is the given…