Browsing by Author "Weber, Gerhard-Wilhelm"

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Citation - WoS: 3
Citation - Scopus: 6
A Discrete Optimality System for an Optimal Harvesting Problem
(Springer Heidelberg, 2017) Bakan, Hacer Oz; Yilmaz, Fikriye; Weber, Gerhard-Wilhelm
In this paper, we obtain the discrete optimality system of an optimal harvesting problem. While maximizing a combination of the total expected utility of the consumption and of the terminal size of a population, as a dynamic constraint, we assume that the density of the population is modeled by a stochastic quasi-linear heat equation. Finite-difference and symplectic partitioned Runge-Kutta (SPRK) schemes are used for space and time discretizations, respectively. It is the first time that a SPRK scheme is employed for the optimal control of stochastic partial differential equations. Monte-Carlo simulation is applied to handle expectation appearing in the cost functional. We present our results together with a numerical example. The paper ends with a conclusion and an outlook to future studies, on further research questions and applications.
Citation - WoS: 10
Citation - Scopus: 11
Minimal Truncation Error Constants for Runge-Kutta Method for Stochastic Optimal Control Problems
(Elsevier, 2018) Bakan, Hacer Oz; Bakan, Hacer Öz; Yilmaz, Fikriye; Weber, Gerhard-Wilhelm; Bakan, Hacer Öz; Mathematics; Mathematics
In this work, we obtain strong order-1 conditions with minimal truncation error constants of Runge-Kutta method for the optimal control of stochastic differential equations (SDEs). We match Stratonovich-Taylor expansion of the exact solution with Stratonovich-Taylor expansion of our approximation method that is defined by the Runge-Kutta scheme, term by term, in order to get the strong order-1 conditions. By a conclusion and an outlook to future research, the paper ends. (C) 2017 Elsevier B.V. All rights reserved.
Citation - WoS: 17
Citation - Scopus: 17
A New Outlier Detection Method Based on Convex Optimization: Application To Diagnosis of Parkinson's Disease
(Taylor & Francis Ltd, 2021) Taylan, Pakize; Yerlikaya-Ozkurt, Fatma; Bilgic Ucak, Burcu; Weber, Gerhard-Wilhelm
Neuroscience is a combination of different scientific disciplines which investigate the nervous system for understanding of the biological basis. Recently, applications to the diagnosis of neurodegenerative diseases like Parkinson's disease have become very promising by considering different statistical regression models. However, well-known statistical regression models may give misleading results for the diagnosis of the neurodegenerative diseases when experimental data contain outlier observations that lie an abnormal distance from the other observation. The main achievements of this study consist of a novel mathematics-supported approach beside statistical regression models to identify and treat the outlier observations without direct elimination for a great and emerging challenge in humankind, such as neurodegenerative diseases. By this approach, a new method named as CMTMSOM is proposed with the contributions of the powerful convex and continuous optimization techniques referred to as conic quadratic programing. This method, based on the mean-shift outlier regression model, is developed by combining robustness of M-estimation and stability of Tikhonov regularization. We apply our method and other parametric models on Parkinson telemonitoring dataset which is a real-world dataset in Neuroscience. Then, we compare these methods by using well-known method-free performance measures. The results indicate that the CMTMSOM method performs better than current parametric models.