Related papers: Tight Semidefinite Relaxations for Verifying Robus…
The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…
The sensor network localization, SNL, problem in embedding dimension r, consists of locating the positions of wireless sensors, given only the distances between sensors that are within radio range and the positions of a subset of the…
Deep Neural Networks (DNNs) have become key components of many safety-critical applications such as autonomous driving and medical diagnosis. However, DNNs have been shown suffering from poor robustness because of their susceptibility to…
Deep learning has become a promising programming paradigm in software development, owing to its surprising performance in solving many challenging tasks. Deep neural networks (DNNs) are increasingly being deployed in practice, but are…
There is an increasing interest in quantum algorithms for optimization problems. Within convex optimization, interior-point methods and other recently proposed quantum algorithms are non-trivial to implement on noisy quantum devices. Here,…
The ubiquity of deep learning algorithms in various applications has amplified the need for assuring their robustness against small input perturbations such as those occurring in adversarial attacks. Existing complete verification…
The Survivable Network Design problem (SNDP) is a well-studied problem, motivated by the design of networks that are robust to faults under the assumption that any subset of edges up to a specific number can fail. We consider non-uniform…
The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's…
We consider the problem of estimating the locations of a set of points in a k-dimensional euclidean space given a subset of the pairwise distance measurements between the points. We focus on the case when some fraction of these measurements…
Computing the key rate in quantum key distribution (QKD) protocols is a long standing challenge. Analytical methods are limited to a handful of protocols with highly symmetric measurement bases. Numerical methods can handle arbitrary…
The success of Deep Learning and its potential use in many safety-critical applications has motivated research on formal verification of Neural Network (NN) models. Despite the reputation of learned NN models to behave as black boxes and…
Semidefinite programs (SDPs) -- some of the most useful and versatile optimization problems of the last few decades -- are often pathological: the optimal values of the primal and dual problems may differ and may not be attained. Such SDPs…
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…
This note uses the Total Least-Squares (TLS) line-fitting problem as a canvas to explore some modern optimization tools. The contribution is meant to be tutorial in nature. The TLS problem has a lot of mathematical similarities to important…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
Semidefinite programs are convex optimisation problems involving a linear objective function and a domain of positive semidefinite matrices. Over the last two decades, they have become an indispensable tool in quantum information science.…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
We explore some connections between association schemes and the analyses of the semidefinite programming (SDP) based convex relaxations of combinatorial optimization problems in the Lov\'{a}sz--Schrijver lift-and-project hierarchy. Our…
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
This paper introduces a stratification framework for nonlinear semidefinite programming (NLSDP) that reveals and utilizes the geometry behind the nonsmooth KKT system. Based on the \emph{index stratification} of $\mathbb{S}^n$ and its lift…