scholarly journals Near-optimality of linear recovery from indirect observations

2018 ◽  
Vol 1 (2) ◽  
pp. 171-225
Author(s):  
Anatoli Juditsky ◽  
Arkadi Nemirovski
Keyword(s):  
Near Optimality

scholarly journals Near Optimality of Linear Delayed Doubly Stochastic Control Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jie Xu ◽  
Ruiqiang Lin
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Control Problem ◽  
Delay System ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
The Maximum Principle ◽  
Doubly Stochastic ◽  
Convex Control ◽  
Near Optimality

In this paper, we study a kind of near optimal control problem which is described by linear quadratic doubly stochastic differential equations with time delay. We consider the near optimality for the linear delayed doubly stochastic system with convex control domain. We discuss the case that all the time delay variables are different. We give the maximum principle of near optimal control for this kind of time delay system. The necessary condition for the control to be near optimal control is deduced by Ekeland’s variational principle and some estimates on the state and the adjoint processes corresponding to the system.

scholarly journals The critical radius in sampling-based motion planning

2019 ◽  
Vol 39 (2-3) ◽  
pp. 266-285 ◽  
Author(s):  
Kiril Solovey ◽  
Michal Kleinbort
Keyword(s):  
Motion Planning ◽  
Critical Radius ◽  
Practical Implication ◽  
Subsequent Work ◽  
Probabilistic Roadmap ◽  
Probability Of Success ◽  
Explicit Lower Bound ◽  
Uniform Random Sampling ◽  
Similar Theory ◽  
Near Optimality

We develop a new analysis of sampling-based motion planning in Euclidean space with uniform random sampling, which significantly improves upon the celebrated result of Karaman and Frazzoli and subsequent work. In particular, we prove the existence of a critical connection radius proportional to [Formula: see text] for n samples and d dimensions: below this value the planner is guaranteed to fail (similarly shown by Karaman and Frazzoli). More importantly, for larger radius values the planner is asymptotically (near-)optimal. Furthermore, our analysis yields an explicit lower bound of [Formula: see text] on the probability of success. A practical implication of our work is that asymptotic (near-)optimality is achieved when each sample is connected to only [Formula: see text] neighbors. This is in stark contrast to previous work that requires [Formula: see text] connections, which are induced by a radius of order [Formula: see text]. Our analysis applies to the probabilistic roadmap method (PRM), as well as a variety of “PRM-based” planners, including RRG, FMT*, and BTT. Continuum percolation plays an important role in our proofs. Lastly, we develop similar theory for all the aforementioned planners when constructed with deterministic samples, which are then sparsified in a randomized fashion. We believe that this new model, and its analysis, is interesting in its own right.

Near-Optimality in Stochastic Control of an Capital Accumulation System with Markovian Switching and Poisson Jumps

2013 ◽  
Vol 300-301 ◽  
pp. 627-630
Author(s):  
Ya Ting Liu ◽  
Qi Min Zhang
Keyword(s):  
Variational Principle ◽  
Stochastic Control ◽  
Capital Accumulation ◽  
Control Variable ◽  
The State ◽  
Markovian Switching ◽  
Necessary Condition ◽  
Poisson Jumps ◽  
Accumulation System ◽  
Near Optimality

We introduce a class of stochastic capital system with Marvokian switching and Poisson jumps, establish necessary condition for near-optimality. The proof of the main results is based on Ito's formula, Ekeland's variational principle and some estimates on the state and the adjoint process with respect to the control variable.

Working sets and near-optimality

1983 ◽  
Vol 17 (3) ◽  
pp. 24-29
Author(s):  
H. Schmutz ◽  
P. Silberbusch
Keyword(s):  
Near Optimality
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