相关论文: Tutorial on the Robust Interior Point Method

This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the…

Primal-dual interior-point methods solve constrained convex optimization problems to tight tolerances with speed and robustness. Their solutions are also efficiently differentiable with respect to the problem data through the implicit…

We present a study on strong t-continuity and measure of discontinuity on PN spaces. As an application, we prove a fixed point theorem for a self mapping on PN spaces by means of measure of discontinuity.

In this paper, we consider the problem of computing robust controlled invariants for discrete-time monotone dynamical systems. We consider different classes of monotone systems depending on whether the sets of states, control inputs and…

We extend the classical primal-dual interior point method from the Euclidean setting to the Riemannian one. Our method, named the Riemannian interior point method, is for solving Riemannian constrained optimization problems. We establish…

This paper considers a class of convex optimization problems where both, the objective function and the constraints, have a continuously varying dependence on time. Our goal is to develop an algorithm to track the optimal solution as it…

Linear programming is now included in algorithm undergraduate and postgraduate courses for computer science majors. We give a self-contained treatment of an interior-point method which is particularly tailored to the typical mathematical…

With the rise of deep neural networks, the challenge of explaining the predictions of these networks has become increasingly recognized. While many methods for explaining the decisions of deep neural networks exist, there is currently no…

Based on existing ideas in the field of imprecise probabilities, we present a new approach for assessing the reliability of the individual predictions of a generative probabilistic classifier. We call this approach robustness…

This paper clarifies the method described in our previous paper (DOI: 978-3-319-02726-5\_21), namely rainbow distinguished point method, and give revised theoretical and experimental results which shows rainbow distinguished point method…

This work addresses the certification of the local robustness of vision-based two-stage 6D object pose estimation. The two-stage method for object pose estimation achieves superior accuracy by first employing deep neural network-driven…

This paper deals with Interior Point Methods (IPMs) for Optimal Control Problems (OCPs) with pure state and mixed constraints. This paper establishes a complete proof of convergence of IPMs for a general class of OCPs. Convergence results…

This note discusses an essentially decentralized interior point method, which is well suited for optimization problems arising in energy networks. Advantages of the proposed method are guaranteed and fast local convergence also for problems…

In panel data we observe a usually high number N of individuals over a time period T. Even if T is large one often assumes stability of the model over time. We propose a nonparametric and robust test for a change in location and derive its…

In this paper, we proposed an interior point method for constrained optimization, which is characterized by the using of quasi-tangential subproblem. This algorithm follows the main ideas of primal dual interior point methods and…

We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an…

This paper consists of four general parts: convex sets; convex functions; convex optimization; and the interior-point algorithm. I will start by introducing the definition of convex sets and give three common convex set examples which will…

We propose and investigate probabilistic guarantees for the adversarial robustness of classification algorithms. While traditional formal verification approaches for robustness are intractable and sampling-based approaches do not provide…

The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…

Quantum relative entropy optimization refers to a class of convex problems in which a linear functional is minimized over an affine section of the epigraph of the quantum relative entropy function. Recently, the self-concordance of a…