On Upper Bounding Shannon Capacity of Graph Through Generalized Conic Programming

Successive Quadratic Upper-Bounding for Discrete Mean-Risk Minimization and Network Interdiction

The advances in conic optimization have led to its increased utilization for modeling data uncertainty. In particular, conic mean-risk optimization gained prominence in probabilistic and robust optimization. Whereas the corresponding conic models are solved efficiently over convex sets, their discrete counterparts are intractable. In this paper, we give a highly effective successive quadratic upper-bounding procedure for discrete mean-risk minimization problems. The procedure is based on a reformulation of the mean-risk problem through the perspective of its convex quadratic term. Computationa…

Semidefinite approximations of conical hulls of measured sets

Let $C$ be a proper convex cone generated by a compact set which supports a measure $μ$. A construction due to A.Barvinok, E.Veomett and J.B. Lasserre produces, using $μ$, a sequence $(P_k)_{k\in \mathbb{N}}$ of nested spectrahedral cones which contains the cone $C^*$ dual to $C$. We prove convergence results for such sequences of spectrahedra and provide tools for bounding the distance between $P_k$ and $C^*$. These tools are especially useful on cones with enough symmetries and allow us to determine bounds for several cones of interest. We compute such upper bounds for semidefinite approxima…

条件期望锐界估计的广义矩方法

A generalized moment approach to sharp bounds for conditional expectations

本文提出广义矩方法的改编版，利用锥对偶性获得条件期望的锐界，并建立基于矩的分布鲁棒优化框架，用于不确定性下的决策。

最大熵远程采样的超缩放NLP界

The hyper-scaled NLP bound for maximum-entropy remote sampling

针对最大熵远程采样问题，提出基于凸松弛的超缩放NLP界，理论上优于传统互补NLP界，并适用于秩亏协方差矩阵，通过数值实验验证了算法先进性。