Related papers: Refining Ky Fan's majorization relation with linea…
A standard approach to solving optimistic bilevel linear programs (BLPs) is to replace the lower-level problem with its Karush-Kuhn-Tucker (KKT) optimality conditions and reformulate the resulting complementarity constraints using auxiliary…
Knowledge refactoring compresses a logic program by introducing new rules. Current approaches struggle to scale to large programs. To overcome this limitation, we introduce a constrained optimisation refactoring approach. Our first key idea…
We face the problems of correctness, optimality and precision for the static analysis of logic programs, using the theory of abstract interpretation. We propose a framework with a denotational, goal-dependent semantics equipped with two…
In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…
Many applications of denotational semantics, such as higher-order model checking or the complexity of normalization, rely on finite semantics for monomorphic type systems. We exhibit such a finite semantics for a polymorphic purely linear…
We give asymptotically converging semidefinite programming hierarchies of outer bounds on bilinear programs of the form $\mathrm{Tr}\big[M(X\otimes Y)\big]$, maximized with respect to semidefinite constraints on $X$ and $Y$. Applied to the…
Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…
Quantum superposition is often phrased as the ability to add state vectors. In practice, however, the physical quantity is a ray (a rank-one projector), so each input specifies only a projector and leaves a gauge freedom in the phases of…
In this work we initiate a positive semi-definite numerical bootstrap program for multi-point correlators. Considering six-point functions of operators on a line we reformulate the crossing symmetry equation for a pair of comb-channel…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…
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…
We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each $n \geq 2$ we present a convex optimization problem whose optimal value is the largest…
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.…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
We give an intuitive combinatorial proof of Ky Fan's covering lemma based on the Borsuk-Ulam theorem. We then show how this approach can be generalized to Ky Fan's covering lemma for several linear orders.
We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and N=1 superconformal field theories. Using our algorithm,…
The max-relative entropy and the conditional min-entropy it induces have become central to one-shot information theory. Both may be expressed in terms of a conic program over the positive semidefinite cone. Recently, it was shown that the…
We consider quantum-information division, which is characterized by a channel whose outputs have no correlation and are not completely randomized. We show that the quantum-information division is possible in a probabilistic manner by…
We provide evidence that quantum mechanics can be interpreted as a rational algorithm for finding the least complex description for the correlations in the outputs of sensors in a large array. In particular, by comparing the…
The renormalization algorithm based on regularization methods with two regulators is analyzed by means of explicit computations. We show in particular that regularization by higher covariant derivative terms can be complemented with…