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We propose new methodologies in robust optimization that promise greater tractabil-ity, both theoretically and practically than the classical robust framework. We cover a broad range of mathematical optimization problems, including linear optimization (LP), quadratic constrained quadratic optimization (QCQP), general conic optimization including second(More)
The consecutive numbering of the publications is determined by their chronological order. The aim of this preprint series is to make new research rapidly available for scientific discussion. Therefore, the responsibility for the contents is solely due to the authors. The publications will be distributed by the authors. Abstract For piecewise monotone(More)
– For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here " eigenvalue " means eigenvalue of the corresponding Perron-Frobenius operator acting on the space of functions of bounded variation(More)
– We prove stochastic stability of chaotic maps for a general class of Markov random perturbations (including singular ones) satisfying some kind of mixing conditions. One of the consequences of this statement is the proof of Ulam's conjecture about the approximation of the dynamics of a chaotic system by a finite state Markov chain. Conditions under which(More)
In this note we give a computable criterion for a piecewise expanding interval map T to be mixing, which at the same time not only establishes explicit bounds on the spectral gap of the associated Perron Frobenius operator acting on the space of functions of bounded variation, but establishes strict contraction rates for this operator. Of course such a(More)
We construct a mixing continuous piecewise linear map on [−1, 1] with the property that a two-dimensional lattice made of these maps with a linear north and east nearest neighbour coupling admits a phase transition. We also provide a modification of this construction where the local map is an expanding analytic circle map. The basic strategy is borroughed(More)