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The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…
Whenever we use devices to take measurements, calibration is indispensable. While the purpose of calibration is to reduce bias and uncertainty in the measurements, it can be quite difficult, expensive, and sometimes even impossible to…
This paper studies the trajectory tracking and motion control problems for autonomous vehicles (AVs). A parameter adaptive control framework for AVs is proposed to enhance tracking accuracy and yaw stability. While establishing linear…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
The feasibility of uniquely estimating parameters of dynamical systems from observations is a widely discussed aspect of mathematical modelling. Several approaches have been published for analyzing identifiability. However, they are…
The particular symmetry of the random-phase-approximation (RPA) matrix has been utilized in the past to reduce the RPA eigenvalue problem into a symmetric-matrix problem of half the dimension. The condition of positive definiteness of at…
The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of…
With recent progress on fine-tuning language models around a fixed sparse autoencoder, we disentangle the decoder matrix into almost orthogonal features. This reduces interference and superposition between the features, while keeping…
This study develops a framework for a class of constant modulus (CM) optimization problems, which covers binary constraints, discrete phase constraints, semi-orthogonal matrix constraints, non-negative semi-orthogonal matrix constraints,…
This paper presents a scalable and fault-tolerant framework for unmanned aerial vehicle (UAV) mission management in complex and uncertain environments. The proposed approach addresses the computational bottleneck inherent in solving…
Mean-reverting portfolios with few assets, but high variance, are of great interest for investors in financial markets. Such portfolios are straightforwardly profitable because they include a small number of assets whose prices not only…
Optimisation algorithms designed to work on quantum computers or other specialised hardware have been of research interest in recent years. Many of these solver can only optimise problems that are in binary and quadratic form. Quadratic…
Feedback motion planning over cell decompositions provides a robust method for generating collision-free robot motion with formal guarantees. However, existing algorithms often produce paths with unnecessary bending, leading to slower…
We consider the optimal regulation problem for nonlinear control-affine dynamical systems. Whereas the linear-quadratic regulator (LQR) considers optimal control of a linear system with quadratic cost function, we study polynomial systems…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
In this paper, by using the Brunovsky normal form, we provide a reformulation of the problem consisting in finding the actuator design which minimizes the controllability cost for finite-dimensional linear systems with scalar controls. Such…
Spacecraft are vital to space exploration and are often equipped with lightweight, flexible appendages to meet strict weight constraints. These appendages pose significant challenges for modeling and control due to their inherent…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
We propose a framework for modeling and solving low-rank optimization problems to certifiable optimality. We introduce symmetric projection matrices that satisfy $Y^2=Y$, the matrix analog of binary variables that satisfy $z^2=z$, to model…
This article presents a method for solving large-scale linear inverse problems regular- ized with a nonlinear, edge-preserving penalty term such as the total variation or Perona-Malik. In the proposed scheme, the nonlinearity is handled…