相关论文: The SDP value for random two-eigenvalue CSPs

In this work, we investigate the convergence of numerical approximations to coercivity constants of variational problems. These constants are essential components of rigorous error bounds for reduced-order modeling; extension of these…

This paper is devoted to providing quantitative bounds on the location of eigenvalues, both discrete and embedded, of non self-adjoint Lam\'e operators of elasticity $-\Delta^\ast + V$ in terms of suitable norms of the potential $V$. In…

Constraint satisfaction problems (CSPs) consist of a set of variables taking values from some finite domain and a set of local constraints on these variables. The objective is to find an assignment to the variables that maximizes the…

We establish the well-posedness of stationary solutions for a class of SPDEs with locally monotone coefficients, and prove the Freidlin--Wentzell large deviation principle (LDP) for these stationary solutions. The LDP for the associated…

We suppose the existence of an oracle which solves any semidefinite programming (SDP) problem satisfying Slater's condition simultaneously at its primal and dual sides. We note that such an oracle might not be able to directly solve general…

We present an optimization framework that exhibits dimension-independent convergence on a broad class of semidefinite programs (SDPs). Our approach first regularizes the primal problem with the von Neumann entropy, then solve the…

Second order nonlinear eigenvalue problems are considered for which the spectrum is an interval. The boundary conditions are of Robin and Dirichlet type. The shape and the number of solutions are discussed by means of a phase plane…

We consider a symmetric block operator spectral problem with two spectral parameters. Under some reasonable restrictions, we state localisation theorems for the pair-eigenvalues and discuss relations to a class of non-self-adjoint spectral…

We study the connection between the order of phase transitions in combinatorial problems and the complexity of decision algorithms for such problems. We rigorously show that, for a class of random constraint satisfaction problems, a limited…

We propose a new kind of stochastic absolute value equations involving absolute values of variables. By utilizing an equivalence relation to stochastic bilinear program, we investigate the expected value formulation for the proposed…

The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…

We initiate the study of spectral sparsification for instances of Constraint Satisfaction Problems (CSPs). In particular, we introduce a notion of the \emph{spectral energy} of a fractional assignment for a Boolean CSP instance, and define…

We prove a probabilistic level-spacing estimate at the bottom of the spectrum for continuum alloy-type random Schr\"odinger operators, assuming sign-definiteness of a single-site bump function and absolutely continuous randomness. More…

Several probabilistic models from high-dimensional statistics and machine learning reveal an intriguing --and yet poorly understood-- dichotomy. Either simple local algorithms succeed in estimating the object of interest, or even…

We establish that the subgame perfect equilibrium (SPE) threshold problem for mean-payoff games is NP-complete. While the SPE threshold problem was recently shown to be decidable (in doubly exponential time) and NP-hard, its exact worst…

Let $f$ be a primitive Maass cusp form for a congruence subgroup $\Gamma_0(D) \subset $ SL($2,\mathbb{Z}$) and $\lambda_f(n)$ its $n$-th Fourier coefficient. In this paper it is shown that with knowledge of only finitely many $\lambda_f(n)$…

The study of phase transition phenomenon of NP complete problems plays an important role in understanding the nature of hard problems. In this paper, we follow this line of research by considering the problem of counting solutions of…

In this paper we show that the Cahn-Hilliard stochastic SPDE has a function valued solution in dimension 4 and 5 when the perturbation is driven by a space-correlated Gaussian noise. This is done proving general results on SPDEs with…

We study interactions between Skolem Arithmetic and certain classes of Constraint Satisfaction Problems (CSPs). We revisit results of Glass er et al. in the context of CSPs and settle the major open question from that paper, finding a…

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP…