Linear-quadratic optimization problem and the frequency theorem for periodic systems. II

1991 ◽  
Vol 31 (6) ◽  
pp. 1027-1039 ◽  
Author(s):  
V. A. Yakubovich
Keyword(s):  
Optimization Problem ◽  
Quadratic Optimization ◽  
Periodic Systems ◽  
Linear Quadratic ◽  
Quadratic Optimization Problem ◽  
Frequency Theorem

Trust Your Data or Not—StQP Remains StQP: Community Detection via Robust Standard Quadratic Optimization

2020 ◽  
Author(s):  
Immanuel M. Bomze ◽  
Michael Kahr ◽  
Markus Leitner
Keyword(s):  
Community Detection ◽  
Optimization Problem ◽  
Quadratic Optimization ◽  
Quadratic Optimization Problem ◽  
Standard Quadratic Optimization ◽  
Uncertainty Sets ◽  
Indefinite Quadratic Form ◽  
Indefinite Quadratic ◽  
Order Intervals ◽  
Copositive Matrix

We consider the robust standard quadratic optimization problem (RStQP), in which an uncertain (possibly indefinite) quadratic form is optimized over the standard simplex. Following most approaches, we model the uncertainty sets by balls, polyhedra, or spectrahedra, more generally, by ellipsoids or order intervals intersected with subcones of the copositive matrix cone. We show that the copositive relaxation gap of the RStQP equals the minimax gap under some mild assumptions on the curvature of the aforementioned uncertainty sets and present conditions under which the RStQP reduces to the standard quadratic optimization problem. These conditions also ensure that the copositive relaxation of an RStQP is exact. The theoretical findings are accompanied by the results of computational experiments for a specific application from the domain of graph clustering, more precisely, community detection in (social) networks. The results indicate that the cardinality of communities tend to increase for ellipsoidal uncertainty sets and to decrease for spectrahedral uncertainty sets.

scholarly journals Virtual Strategy Engineer: Using Artificial Neural Networks for Making Race Strategy Decisions in Circuit Motorsport

2020 ◽  
Vol 10 (21) ◽  
pp. 7805
Author(s):  
Alexander Heilmeier ◽  
André Thomaser ◽  
Michael Graf ◽  
Johannes Betz
Keyword(s):  
Neural Networks ◽  
Artificial Neural Networks ◽  
Optimization Problem ◽  
Quadratic Optimization ◽  
High Class ◽  
Simplified Approach ◽  
Quadratic Optimization Problem ◽  
Timing Data ◽  
Strategic Options ◽  
Artificial Neural

In circuit motorsport, race strategy helps to finish the race in the best possible position by optimally determining the pit stops. Depending on the racing series, pit stops are needed to replace worn-out tires, refuel the car, change drivers, or repair the car. Assuming a race without opponents and considering only tire degradation, the optimal race strategy can be determined by solving a quadratic optimization problem, as shown in the paper. In high-class motorsport, however, this simplified approach is not sufficient. There, comprehensive race simulations are used to evaluate the outcome of different strategic options. The published race simulations require the user to specify the expected strategies of all race participants manually. In such simulations, it is therefore desirable to automate the strategy decisions, for better handling and greater realism. It is against this background that we present a virtual strategy engineer (VSE) based on two artificial neural networks. Since our research is focused on the Formula 1 racing series, the VSE decides whether a driver should make a pit stop and which tire compound to fit. Its training is based on timing data of the six seasons from 2014 to 2019. The results show that the VSE makes reasonable decisions and reacts to the particular race situation. The integration of the VSE into a race simulation is presented, and the effects are analyzed in an example race.

scholarly journals Linear-quadratic optimization and some general hypotheses on optimal control

1999 ◽  
Vol 5 (4) ◽  
pp. 275-289 ◽  
Author(s):  
L. I. Rozonoer
Keyword(s):  
Optimal Control ◽  
Initial Data ◽  
Optimization Problem ◽  
Sufficient Conditions ◽  
Quadratic Optimization ◽  
Necessary And Sufficient Conditions ◽  
Maximum Condition ◽  
Linear Quadratic ◽  
Existence Of Optimal Control ◽  
Necessary And Sufficient

Necessary and sufficient conditions for existence of optimal control for all initial data are proved forLQ-optimization problem. If these conditions are fulfilled, necessary and sufficient conditions of optimality are formulated. Basing on the results, some general hypotheses on optimal control in terms of Pontryagin's maximum condition and Bellman's equation are proposed.

scholarly journals A duality-type method for the obstacle problem

2013 ◽  
Vol 21 (3) ◽  
pp. 181-196 ◽  
Author(s):  
Diana Rodica Merlusca
Keyword(s):  
Sobolev Spaces ◽  
Obstacle Problem ◽  
Optimization Problem ◽  
Quadratic Optimization ◽  
Higher Order ◽  
Type Method ◽  
Quadratic Optimization Problem ◽  
Approximate Problem ◽  
Duality Property ◽  
New Type

Abstract Based on a duality property, we solve the obstacle problem on Sobolev spaces of higher order. We have considered a new type of approximate problem and with the help of the duality we reduce it to a quadratic optimization problem, which can be solved much easier.

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