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In this survey we review the many faces of the S-lemma, a result about the cor-rectness of the S-procedure. The basic idea of this widely used method came from control theory but it has important consequences in quadratic and semidefinite optimization, convex geometry and linear algebra as well. These were active research areas, but as there was little(More)
We investigate families of quadrics that have fixed intersections with two given hyper-planes. The cases when the two hyperplanes are parallel and when they are nonparallel are discussed. We show that these families can be described with only one parameter. In particular we show how the quadrics are transformed as the parameter changes. This research was(More)
Detecting infeasibility in conic optimization and providing certificates for infea-sibility pose a bigger challenge than in the linear case due to the lack of strong duality. In this paper we generalize the approximate Farkas lemma of Todd and Ye [12] from the linear to the general conic setting, and use it to propose stopping criteria for interior point(More)
In this paper we introduce a novel reinforcement learning algorithm called event-learning. The algorithm uses events, ordered pairs of two consecutive states. We define event-value function and we derive learning rules. Combining our method with a well-known robust control method, the SDS algorithm, we introduce Robust Policy Heuristics (RPH). It is shown(More)
The following question arises in stochastic programming: how can one approximate a noisy convex function with a convex quadratic function that is optimal in some sense. Using several approaches for constructing convex approximations we present some optimization models yielding convex quadratic regressions that are optimal approximations in L 1 , L∞ and L 2(More)
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