Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral am...

Any reliable model for scheduling optical space-to-ground communication must factor in cloud cover conditions due to attenuation of the laser beam by water droplets clouds. In this article, we provide two alternative models uncertainty predictions: a robust optimization with polyhedral set and distributionally moment-based ambiguity set. We computationally analyze their performance over realist...

The 3-D reconstruction of visible polyhedral faces from a pair of general perspective views with the aid of a calibration plate is addressed. A polyhedron is placed on a planar calibration plate and two side views of both the polyhedron and the calibration plate are taken. Through proper arrangements we may assume that in the two views a number of polyhedral edges lying on the calibration plate...

A computational method is developed for solving time consistent distributionally robust multistage stochastic linear programs with discrete distribution. The structure of the uncertain parameters described by a scenario tree. At each node this tree, an ambiguity set defined conditional moment constraints to guarantee consistency. This employs idea nested Benders decomposition that incorporates ...

We study a generalized distributionally robust chance-constrained set covering problem (DRC) with Wasserstein ambiguity set, where both decisions and uncertainty are binary-valued. establish the NP-hardness of DRC recast it as two-stage stochastic program, which facilitates decomposition algorithms. Furthermore, we derive two families valid inequalities. The first family targets hypograph “shif...

We adapt the method of Simon [26] to prove a $C^{1,\alpha}$-regularity theorem for minimal varifolds which resemble cone $\mathbf{C}^2_0$ over an equiangular geodesic net. For varifold classes admitting “no-hole” condition on singular set, we additionally establish near $\mathbf{C}^2_0 \times \mathbb{R}^m$. Combined with work Allard [2], [26], Taylor [29], and Naber–Valtorta [21], our result im...