scholarly journals Application of maximal monotone operator method for solving Hamilton–Jacobi–Bellman equation arising from optimal portfolio selection problem

Author(s):  
Cyril Izuchukwu Udeani ◽  
Daniel Ševčovič
Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1395
Author(s):  
Charles Castaing ◽  
Christiane Godet-Thobie ◽  
Le Xuan Truong

This paper is devoted to the study of evolution problems involving fractional flow and time and state dependent maximal monotone operator which is absolutely continuous in variation with respect to the Vladimirov’s pseudo distance. In a first part, we solve a second order problem and give an application to sweeping process. In a second part, we study a class of fractional order problem driven by a time and state dependent maximal monotone operator with a Lipschitz perturbation in a separable Hilbert space. In the last part, we establish a Filippov theorem and a relaxation variant for fractional differential inclusion in a separable Banach space. In every part, some variants and applications are presented.


2021 ◽  
pp. 1-14
Author(s):  
Daniel Saranovic ◽  
Martin Pavlovski ◽  
William Power ◽  
Ivan Stojkovic ◽  
Zoran Obradovic

As the prevalence of drones increases, understanding and preparing for possible adversarial uses of drones and drone swarms is of paramount importance. Correspondingly, developing defensive mechanisms in which swarms can be used to protect against adversarial Unmanned Aerial Vehicles (UAVs) is a problem that requires further attention. Prior work on intercepting UAVs relies mostly on utilizing additional sensors or uses the Hamilton-Jacobi-Bellman equation, for which strong conditions need to be met to guarantee the existence of a saddle-point solution. To that end, this work proposes a novel interception method that utilizes the swarm’s onboard PID controllers for setting the drones’ states during interception. The drone’s states are constrained only by their physical limitations, and only partial feedback of the adversarial drone’s positions is assumed. The new framework is evaluated in a virtual environment under different environmental and model settings, using random simulations of more than 165,000 swarm flights. For certain environmental settings, our results indicate that the interception performance of larger swarms under partial observation is comparable to that of a one-drone swarm under full observation of the adversarial drone.


2010 ◽  
Vol 83 (1) ◽  
pp. 22-29 ◽  
Author(s):  
FILOMENA CIANCIARUSO ◽  
GIUSEPPE MARINO ◽  
LUIGI MUGLIA ◽  
HONG-KUN XU

AbstractWe construct a sequence {An} of maximal monotone operators with a common domain and converging, uniformly on bounded subsets, to another maximal monotone operator A; however, the sequence {t−1nAn} fails to graph-converge for some null sequence {tn}.


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