One-step extension approach to optimal Hankel-norm approximation and H/sup infinity /-optimization problems

1993 ◽  
Vol 38 (5) ◽  
pp. 674-688 ◽  
Author(s):  
Ciann-Dong Yang ◽  
Fang-Bo Yeh
Keyword(s):  
Optimization Problems ◽  
One Step ◽  
Hankel Norm ◽  
Norm Approximation

On the transformation formulas of the Hankel-norm approximation

PAMM ◽  
2017 ◽  
Vol 17 (1) ◽  
pp. 823-824
Author(s):  
Peter Benner ◽  
Steffen W. R. Werner
Keyword(s):  
Hankel Norm ◽  
Transformation Formulas ◽  
Norm Approximation

Hankel-Norm Approximation of IIR by FIR Models: A Constructive Method

2008 ◽  
Vol 55 (2) ◽  
pp. 586-598 ◽  
Author(s):  
Li Chai ◽  
Jingxin Zhang ◽  
Cishen Zhang ◽  
E. Mosca
Keyword(s):  
Constructive Method ◽  
Hankel Norm ◽  
Norm Approximation

scholarly journals Reinforcement Learning for Route Optimization with Robustness Guarantees

2021 ◽  
Author(s):  
Tobias Jacobs ◽  
Francesco Alesiani ◽  
Gulcin Ermis
Keyword(s):  
Reinforcement Learning ◽  
Optimization Problems ◽  
Route Optimization ◽  
Research Trend ◽  
Learning To Learn ◽  
Combinatorial Optimization Problems ◽  
One Step ◽  
Full Solution ◽  
Original Objective ◽  
The One

Application of deep learning to NP-hard combinatorial optimization problems is an emerging research trend, and a number of interesting approaches have been published over the last few years. In this work we address robust optimization, which is a more complex variant where a max-min problem is to be solved. We obtain robust solutions by solving the inner minimization problem exactly and apply Reinforcement Learning to learn a heuristic for the outer problem. The minimization term in the inner objective represents an obstacle to existing RL-based approaches, as its value depends on the full solution in a non-linear manner and cannot be evaluated for partial solutions constructed by the agent over the course of each episode. We overcome this obstacle by defining the reward in terms of the one-step advantage over a baseline policy whose role can be played by any fast heuristic for the given problem. The agent is trained to maximize the total advantage, which, as we show, is equivalent to the original objective. We validate our approach by solving min-max versions of standard benchmarks for the Capacitated Vehicle Routing and the Traveling Salesperson Problem, where our agents obtain near-optimal solutions and improve upon the baselines.

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