区间系统的H ∞性能

H-无限最优分散匹配模型并不总是合理的

H-Infinity Optimal Decentralized Matching Model Is Not Always Rational

构造了具有有理系数的结构化H-Infinity最优模型匹配问题，其中的最优解不是有理的，即费用在有理匹配模型集上不能达到其最大下界，但在连续的非有理匹配模型下可以达到同样的最大下界.

Maximal determinants of Schrödinger operators on bounded intervals

We consider the problem of finding extremal potentials for the functional determinant of a one-dimensional Schrödinger operator defined on a bounded interval with Dirichlet boundary conditions under an $L^q$-norm restriction ($q\geq 1$). This is done by first extending the definition of the functional determinant to the case of $L^q$ potentials and showing the resulting problem to be equivalent to a problem in optimal control, which we believe to be of independent interest. We prove existence, uniqueness and describe some basic properties of solutions to this problem for all $q\geq 1$, providi…

The NP-hard problem of computing the maximal sample variance over interval data is solvable in almost linear time with high probability

We consider the algorithm by Ferson et al. (Reliable computing 11(3), p. 207-233, 2005) designed for solving the NP-hard problem of computing the maximal sample variance over interval data, motivated by robust statistics (in fact, the formulation can be written as a nonconvex quadratic program with a specific structure). First, we propose a new version of the algorithm improving its original time bound $O(n^2 2^ω)$ to $O(n \log n+n\cdot 2^ω)$, where $n$ is number of input data and $ω$ is the clique number in a certain intersection graph. Then we treat input data as random variables as it is us…

Improving and benchmarking of algorithms for decision making with lower previsions

Maximality, interval dominance, and E-admissibility are three well-known criteria for decision making under severe uncertainty using lower previsions. We present a new fast algorithm for finding maximal gambles. We compare its performance to existing algorithms, one proposed by Troffaes and Hable (2014), and one by Jansen, Augustin, and Schollmeyer (2017). To do so, we develop a new method for generating random decision problems with pre-specified ratios of maximal and interval dominant gambles. Based on earlier work, we present efficient ways to find common feasible starting points in these a…