Image compression by means of the multidimensional circulant covariance extension problem -- Revisited

Multidimensional free-mobility equilibrium: Tiebout revisited

The paper provides consistent mathematical framework for seminal Tiebout free-mobility model (1956). Our setting supports continuum of consumers with multidimensional preferences and finite number of strategic public good providers. We accommodate the most general assumptions: providers' production function may have variable returns to scale, our framework is rich enough to incorporate possible externalities, spillovers, scale economies, network effects, etc.; consumers utility may depend on choice of other agents in almost arbitrary way. We focus on equilibrium existence, however the question…

The Time-Invariant Multidimensional Gaussian Sequential Rate-Distortion Problem Revisited

We revisit the sequential rate-distortion (SRD) trade-off problem for vector-valued Gauss-Markov sources with mean-squared error distortion constraints. We show via a counterexample that the dynamic reverse water-filling algorithm suggested by [1, eq. (15)] is not applicable to this problem, and consequently the closed form expression of the asymptotic SRD function derived in [1, eq. (17)] is not correct in general. Nevertheless, we show that the multidimensional Gaussian SRD function is semidefinite representable and thus it is readily computable.

最优控制曲面的多维傅里叶逼近

A Multidimensional Fourier Approximation of Optimal Control Surfaces

本研究提出改进增广拉格朗日算法，结合多元傅里叶级数逼近最优控制与轨迹曲面，引入自动微分简化梯度计算，推导了不同维度下的均方误差界，为多类最优控制问题提供高效求解方案。