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We study the computational complexity certification of inexact gradient augmented Lagrangian methods for solving convex optimization problems with complicated constraints. We solve the augmented Lagrangian dual problem that arises from the…
A classic result of Cook et al. (1986) bounds the distances between optimal solutions of mixed-integer linear programs and optimal solutions of the corresponding linear relaxations. Their bound is given in terms of the number of variables…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the…
Consider a matrix polynomial $P \left( \lambda \right)= A_0 + \lambda A_1 + \ldots + \lambda^d A_d$, with $A_0,\ldots, A_d$ complex (or real) matrices with a certain structure. In this paper we discuss an iterative method to numerically…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
We consider the problem of model reduction of parametrized PDEs where the goal is to approximate any function belonging to the set of solutions at a reduced computational cost. For this, the bottom line of most strategies has so far been…
High-dimensional nonlinear optimization problems subject to nonlinear constraints can appear in several contexts including constrained physical and dynamical systems, statistical estimation, and other numerical models. Feasible optimization…
We consider a new class of Parareal algorithms, which use ideas from localized reduced basis methods to construct the coarse solver from spectral approximations of the transfer operators mapping initial values for a given time interval to…
We study several versions of the alternating direction method of multipliers (ADMM) for solving the convex problem of finding the distance between two ellipsoids and the nonconvex problem of finding the distance between the boundaries of…
This paper studies binary quadratic programs in which the objective is defined by a Euclidean distance matrix, subject to a general polyhedral constraint set. This class of nonconcave maximisation problems includes the capacitated,…
Precise sensor calibration is critical for autonomous vehicles as a prerequisite for perception algorithms to function properly. Rotation error of one degree can translate to position error of meters in target object detection at large…
We present a method of extrinsic calibration for a system of multiple inertial measurement units (IMUs) that estimates the relative pose of each IMU on a rigid body using only measurements from the IMUs themselves, without the need to…
Integer semidefinite programming (ISDP) has recently gained attention due to its connection to binary quadratically constrained quadratic programs (BQCQPs), which can be exactly reformulated as binary semidefinite programs (BSDPs). However,…
Path planning for multiple robots is well studied in the AI and robotics communities. For a given discretized environment, robots need to find collision-free paths to a set of specified goal locations. Robots can be fully anonymous,…
Simulation is useful for the evaluation of a Master Production/distribution Schedule (MPS). Also, the goal of this paper is the study of the design of a simulation model by reducing its complexity. According to theory of constraints, we…
We present a method of computing backward reachable sets for nonlinear discrete-time control systems possessing continuous symmetries. The starting point is a dynamic game formulation of reachability analysis where control inputs aim to…
This paper proposes and analyzes a dampened proximal alternating direction method of multipliers (DP.ADMM) for solving linearly-constrained nonconvex optimization problems where the smooth part of the objective function is nonseparable.…
The input to the distant representatives problem is a set of $n$ objects in the plane and the goal is to find a representative point from each object while maximizing the distance between the closest pair of points. When the objects are…
With increasing use of digital control it is natural to view control inputs and outputs as stochastic processes assuming values over finite alphabets rather than in a Euclidean space. As control over networks becomes increasingly common,…