Related papers: On second-order cone positive systems
We consider linear recurrences with polynomial coefficients of Poincar\'e type and with a unique simple dominant eigenvalue. We give an algorithm that proves or disproves positivity of solutions provided the initial conditions satisfy a…
Quantum communication with systems of dimension larger than two provides advantages in information processing tasks. Examples include higher rates of key distribution and random number generation. The main disadvantage of using such…
We propose a tutorial on relaxations and weak formulations of optimal control with their semidefinite approximations. We present this approach solely through the prism of positivity certificates which we consider to be the most accessible…
Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…
We discuss optimization problems over convex cones in which membership is difficult to verify directly. In the standard theory of duality, vectors in the dual cone $K^*$ are associated with separating hyperplanes and interpreted as…
In this paper, we present an impulse response identification scheme that incorporates the internal positivity side-information of the system. The realization theory of positive systems establishes specific criteria for the existence of a…
It is well-known that the second-order cone can be outer-approximated to an arbitrary accuracy $\epsilon$ by a polyhedral cone of compact size defined by irrational data. In this paper, we propose two rational polyhedral…
We revisit the problem of property testing for convex position for point sets in $\mathbb{R}^d$. Our results draw from previous ideas of Czumaj, Sohler, and Ziegler (ESA 2000). First, the algorithm is redesigned and its analysis is revised…
We study the problem of computing weighted sum-of-squares (WSOS) certificates for positive polynomials over a compact semialgebraic set. Building on the theory of interior-point methods for convex optimization, we introduce the concept of…
An efficient intuitionistic first-order prover integrated into Coq is useful to replay proofs found by external automated theorem provers. We propose a two-phase approach: An intuitionistic prover generates a certificate based on the matrix…
This paper is devoted to the generalized differential study of the normal cone mappings associated with a large class of parametric constraint systems (PCS) that appear, in particular, in nonpolyhedral conic programming. Conducting a local…
Reliable randomness is a core ingredient in algorithms and applications ranging from numerical simulations to statistical sampling and cryptography. The outcomes of measurements on entangled quantum states can violate Bell inequalities,…
Certification of quantum devices received from unknown providers is a primary requirement before utilizing the devices for any information processing task. Here, we establish a protocol for certification of a particular set of $d$-outcome…
The performance of a reinforcement learning algorithm can vary drastically during learning because of exploration. Existing algorithms provide little information about the quality of their current policy before executing it, and thus have…
Using the dual cone of sums of nonnegative circuits (SONC), we provide a relaxation of the global optimization problem to minimize an exponential sum and, as a special case, a multivariate real polynomial. Our approach builds on two key…
We consider decision-making problems that are formulated as non-convex optimization programs where uncertainty enters the constraints through an additive term, independent of the decision variables, and robustness is imposed using a finite…
The generation of certifiable randomness is one of the most promising applications of quantum technologies. Furthermore, the intrinsic non-locality of quantum correlations allow us to certify randomness in a device-independent way, i.e. one…
This paper proposes an efficient algorithm for testing copositivity of homogeneous polynomials over the positive semidefinite cone. The algorithm is based on a novel matrix optimization reformulation and requires solving a hierarchy of…
Several signal recovery tasks can be relaxed into semidefinite programs with rank-one minimizers. A common technique for proving these programs succeed is to construct a dual certificate. Unfortunately, dual certificates may not exist under…
We demonstrate to what extent many copies of maximally entangled two-qubit states enable for generating a greater amount of certified randomness than that can be certified from a single copy. Although it appears that greater the dimension…