Related papers: Linear programming with unitary-equivariant constr…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
Symmetries occur naturally in CSP or SAT problems and are not very difficult to discover, but using them to prune the search space tends to be very challenging. Indeed, this usually requires finding specific elements in a group of…
As machine learning applications grow increasingly ubiquitous and complex, they face an increasing set of requirements beyond accuracy. The prevalent approach to handle this challenge is to aggregate a weighted combination of requirement…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
The main thrust of our current work is to exploit very specific characteristics of a given problem in order to acquire improved compactness for supercritical problems and to prove existence of new types of solutions. To this end, we shall…
Equivariances provide useful inductive biases in neural network modeling, with the translation equivariance of convolutional neural networks being a canonical example. Equivariances can be embedded in architectures through weight-sharing…
Seeking tighter relaxations of combinatorial optimization problems, semidefinite programming is a generalization of linear programming that offers better bounds and is still polynomially solvable. Yet, in practice, a semidefinite program is…
This paper studies the unification problem with associative, commutative, and associative-commutative functions mainly from a viewpoint of the parameterized complexity on the number of variables. It is shown that both associative and…
The accuracies of modern quantum logic clocks have surpassed those of standard atomic fountain clocks. These clocks also provide a greater degree of control, because before and after clock queries, we are able to apply chosen unitary…
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…
This paper presents an iterative method suitable for inverting semilinear problems which are important kernels in many numerical applications. The primary idea is to employ a parametrization that is able to reduce semilinear problems into…
We study a class of generalized linear programs (GLP) in a large-scale setting, which includes simple, possibly nonsmooth convex regularizer and simple convex set constraints. By reformulating (GLP) as an equivalent convex-concave min-max…
Interest in anti-unification, the dual problem of unification, is on the rise due to applications within the field of software analysis and related areas. For example, anti-unification-based techniques have found uses within clone detection…
A universal quantum processor is a device that takes as input a (quantum) program, containing an encoding of an arbitrary unitary gate, and a (quantum) data register, on which the encoded gate is applied. While no perfect universal quantum…
This paper studies, for the first time, a bilevel polynomial program whose constraints involve uncertain linear constraints and another uncertain linear optimization problem. In the case of box data uncertainty, we present a sum of squares…
We revisit a formulation technique for inequality constrained optimization problems that has been known for decades: the substitution of squared variables for nonnegative variables. Using this technique, inequality constraints are converted…
This paper presents and analyzes the first matrix optimization model which allows general coordinate and spectral constraints. The breadth of problems our model covers is exemplified by a lengthy list of examples from the literature,…
We study robust convex quadratic programs where the uncertain problem parameters can contain both continuous and integer components. Under the natural boundedness assumption on the uncertainty set, we show that the generic problems are…