We consider the Hamiltonian cycle problem (HCP) embedded in a controlled Markov decision process. In this setting, HCP reduces to an optimization problem on a set of Markov chains corresponding to a given graph. We prove that Hamiltonian cycles are minimizers for the trace of the fundamental matrix on a set of all stochastic transition matrices. In case of doubly stochastic matrices with symmet...

We prove strong uniqueness for a parabolic SPDE involving both the solution v(t, x) and its derivative ∂xv(t, x). The familiar YamadaWatanabe method for proving strong uniqueness might encounter some difficulties here. In fact, the Yamada-Watanabe method is essentially one dimensional, and in our case there are two unknown functions, v and ∂xv. However, Pardoux and Peng’s method of backward dou...

Abstract For X, Y ∈ M n,m , it is said that X g-tridiagonal majorized by (and denoted ≺ gt ) if there exists a tridiagonal g-doubly stochastic matrix A such = AY . In this paper, the linear preservers and strong of are characterized on

ABSTRACT. A bivariate distribution with continuous margins can be uniquely decomposed via a copula and its marginal distributions. We consider the problem of estimating the copula function and adopt a nonparametric Bayesian approach. On the space of copula functions, we construct a finite dimensional approximation subspace which is parameterized by a doubly stochastic matrix. A major problem he...

We are interested in the following work in the doubly stochastic matrix nearness problem. Instances of this problems occurs in differents fields: aggregation of preferences in operational research, calculus of variations and shape optimisation, etc. We propose here a direct study via the projection theorem and a numerical resolution inspired by the alternating projections algorithm of Boyle-Dyk...

In graph-based clustering, a relevant affinity matrix is crucial for good results. Double stochasticity of the has been shown to be an important condition, both in theory and practice. this paper, we emphasize idempotency as another key condition. fact, theorem from Sinkhorn, R. (1968) allows us exhibit bijective relationship between set doubly stochastic idempotent matrices order n (modulo per...

We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where nonsingularity of Jacobian can fail. The optimality conditions this are formulated as system strongly functions. show that does not hold system. By exploiting structure, we construct modified two step Newton guarantees nonsingular at each iteration, and converges to quadratically. Funding: This work ...