Related papers: An exact duality theory for semidefinite programmi…

Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model…

In a common formulation of semi-infinite programs, the infinite constraint set is a requirement that a function parametrized by the decision variables is nonnegative over an interval. If this function is sufficiently closely approximable by…

Recently, there is growing concern that machine-learning models, which currently assist or even automate decision making, reproduce, and in the worst case reinforce, bias of the training data. The development of tools and techniques for…

We consider semi-infinite linear programs with countably many constraints indexed by the natural numbers. When the constraint space is the vector space of all real valued sequences, we show the finite support (Haar) dual is equivalent to…

We investigate the use of linear programming tools for solving semidefinite programming relaxations of quadratically constrained quadratic problems. Classes of valid linear inequalities are presented, including sparse PSD cuts, and…

One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…

Matrix-valued polynomials in any finite number of freely noncommuting variables that enjoy certain canonical partial convexity properties are characterized, via an algebraic certificate, in terms of Linear Matrix Inequalities and Bilinear…

We prove that the subset sum problem has a polynomial time computable certificate of infeasibility for all $a$ weight vectors with density at most $1/(2n)$ and for almost all integer right hand sides. The certificate is branching on a…

We consider the stability analysis of a large class of linear 1-D PDEs with polynomial data. This class of PDEs contains, as examples, parabolic and hyperbolic PDEs, PDEs with boundary feedback and systems of in-domain/boundary coupled…

We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function to be optimized. In this paper, we propose an algorithm…

A linear map between matrix spaces is positive if it maps positive semidefinite matrices to positive semidefinite ones, and is called completely positive if all its ampliations are positive. In this article quantitative bounds on the…

Kleene algebra (KA) is an important tool for reasoning about general program equivalences, with a decidable and complete equational theory. However, KA cannot always prove equivalences between specific programs. For this purpose, one adds…

A geometric inequality among three triangles, originating in circle packing problems, is introduced. In order to prove it, we reduce the original formulation to the nonnegativity of a particular polynomial in four real indeterminates.…

Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…

In 1995, Reznick showed an important variant of the obvious fact that any positive semidefinite (real) quadratic form is a sum of squares of linear forms: If a form (of arbitrary even degree) is positive definite then it becomes a sum of…

This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the…

Property A is a form of weak amenability for groups and metric spaces introduced as an approach to the famous Novikov higher signature conjecture, one of the most important unsolved problems in topology. We show that property A can be…

In this paper we introduce a measure of genuine quantum incompatibility in the estimation task of multiple parameters, that has a geometric character and is backed by a clear operational interpretation. This measure is then applied to some…

Let $A(x)=A\_0+x\_1A\_1+...+x\_nA\_n$ be a linear matrix, or pencil, generated by given symmetric matrices $A\_0,A\_1,...,A\_n$ of size $m$ with rational entries. The set of real vectors x such that the pencil is positive semidefinite is a…

We study quasi-exact quantum error correcting codes and quantum computation with them. A quasi-exact code is an approximate code such that it contains a finite number of scaling parameters, the tuning of which can flow it to corresponding…