-
作者：Luke, D. Russell; Thao, Nguyen H.; Tama, Matthew K.
作者单位：University of Gottingen; Delft University of Technology
摘要：We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged mappings to expansive set-valued mappings that characterizes a type of strong calmness of the fixed point mapping. The second component to this analysis is an extension of the well-established notion of metric subregularity-or inverse calmness-of the mapping a...
-
作者：De Angelis, Tiziano; Kitapbayev, Yerkin
作者单位：University of Leeds; Boston University
摘要：We use probabilistic methods to characterise time-dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications, we consider a payoff of immediate stopping of put type, and the underlying dynamics follows a geometric Brownian motion. The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries, which are continuous, monotonic functions of time and uniquely solve a syste...
-
作者：Karmakar, Prasenjit; Bhatnagar, Shalabh
作者单位：Indian Institute of Science (IISC) - Bangalore
摘要：We present for the first time an asymptotic convergence analysis of two time-scale stochastic approximation driven by controlled Markov noise. In particular, the faster and slower recursions have nonadditive controlled Markov noise components in addition to martingale difference noise. We analyze the asymptotic behavior of our framework by relating it to limiting differential inclusions in both time scales that are defined in terms of the ergodic occupation measures associated with the control...
-
作者：Gaudioso, Manlio; Giallombardo, Giovanni; Miglionico, Giovanna
作者单位：University of Calabria
摘要：We introduce an iterative method for solving linearly constrained optimization problems, whose nonsmooth nonconvex objective function is defined as the pointwise maximum of finitely many concave functions. Such problems often arise from reformulations of certain constraint structures (e.g., binary constraints, finite max-min constraints) in diverse areas of optimization. We state a local optimization strategy, which exploits piecewise-concavity of the objective function, giving rise to a linea...
-
作者：Chambers, Christopher P.; Echenique, Federico
作者单位：Georgetown University; California Institute of Technology
摘要：We prove that combinatorial demand functions are characterized by two properties: continuity and the law of demand.
-
作者：Gu, Jia-Wen; Steffensen, Mogens; Zheng, Harry
作者单位：Southern University of Science & Technology; University of Copenhagen; Imperial College London
摘要：In this paper, we consider the optimal dividend payment strategy for an insurance company that has two collaborating business lines. The surpluses of the business lines are modeled by diffusion processes. The collaboration between the two business lines permits that money can be transferred from one line to another with or without proportional transaction costs, while money must be transferred from one line to another to help both business lines keep running before simultaneous ruin of the two...
-
作者：Gillis, Nicolas; Vavasis, Stephen A.
作者单位：University of Mons; University of Waterloo
摘要：The low-rank matrix approximation problem with respect to the component-wise l(1)-norm (l(1)-LRA), which is closely related to robust principal component analysis (PCA), has become a very popular tool in data mining and machine learning. Robust PCA aims to recover a low-rank matrix that was perturbed with sparse noise, with applications for example in foreground-background video separation. Although l(1)-LRA is strongly believed to be NP-hard, there is, to our knowledge, no formal proof of thi...
-
作者：Arapostathis, Ari; Pang, Guodong
作者单位：University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
摘要：We study the infinite-horizon optimal control problem for N-network queueing systems, which consists of two customer classes and two server pools, under average (ergodic) criteria in the Halfin-Whitt regime. We consider three control objectives: (1) minimizing the queueing (and idleness) cost, (2) minimizing the queueing cost while imposing a constraint on idleness at each server pool, and (3) minimizing the queueing cost while requiring fairness on idleness. The running costs can be any nonne...
-
作者：Benchetrit, Yohann; Fiorini, Samuel; Huynh, Tony; Weltge, Stefan
作者单位：Universite Libre de Bruxelles
摘要：Let S subset of {0, 1}(n) and R be any polytope contained in [0, 1](n) with R boolean AND {0, 1}(n) = S. We prove that R has bounded Chvatal-Gomory rank (CG-rank) provided that S has bounded notch and bounded gap, where the notch is the minimum integer p such that all p-dimensional faces of the 0/1-cube have a nonempty intersection with S, and the gap is a measure of the size of the facet coefficients of conv(S). Let H[(S) over bar] denote the subgraph of the n-cube induced by the vertices not...
-
作者：Drusvyatskiy, Dmitriy; Lewis, Adrian S.
作者单位：University of Washington; University of Washington Seattle; Cornell University
摘要：The proximal gradient algorithm for minimizing the sum of a smooth and nonsmooth convex function often converges linearly even without strong convexity. One common reason is that a multiple of the step length at each iteration may linearly bound the error-the distance to the solution set. We explain the observed linear convergence intuitively by proving the equivalence of such an error bound to a natural quadratic growth condition. Our approach generalizes to linear and quadratic convergence ...
