Damped Dynamical Systems for Solving Equations and Optimization Problems

2021 ◽  
pp. 2171-2215
Author(s):  
Mårten Gulliksson ◽  
Magnus Ögren ◽  
Anna Oleynik ◽  
Ye Zhang
Keyword(s):  
Dynamical Systems ◽  
Optimization Problems ◽  
Solving Equations

Damped Dynamical Systems for Solving Equations and Optimization Problems

2018 ◽  
pp. 1-44 ◽  
Author(s):  
Mårten Gulliksson ◽  
Magnus Ögren ◽  
Anna Oleynik ◽  
Ye Zhang
Keyword(s):  
Dynamical Systems ◽  
Optimization Problems ◽  
Solving Equations

scholarly journals Alternated Superior Chaotic Biogeography Based Algorithm for Optimization Problems

2022 ◽  
Vol 13 (1) ◽  
pp. 0-0
Keyword(s):  
Dynamical Systems ◽  
Dynamic Behaviour ◽  
Optimization Problems ◽  
Bifurcation Diagrams ◽  
Switching Strategy ◽  
Alternate Version ◽  
Parrondo’S Paradox ◽  
Stable Periodic ◽  
Parameter Values ◽  
Superior Orbit

In this study, we consider a switching strategy that yields a stable desirable dynamic behaviour when it is applied alternatively between two undesirable dynamical systems. From the last few years, dynamical systems employed “chaos1 + chaos2 = order” and “order1 + order2 = chaos” (vice-versa) to control and anti control of chaotic situations. To find parameter values for these kind of alternating situations, comparison is being made between bifurcation diagrams of a map and its alternate version, which, on their own, means independent of one another, yield chaotic orbits. However, the parameter values yield a stable periodic orbit, when alternating strategy is employed upon them. It is interesting to note that we look for stabilization of chaotic trajectories in nonlinear dynamics, with the assumption that such chaotic behaviour is not desirable for a particular situation. The method described in this paper is based on the Parrondo’s paradox, where two losing games can be alternated, yielding a winning game, in a superior orbit.

scholarly journals Some features of the problems of computational optimization in the computer-integrated systems

2021 ◽  
pp. 64-69
Author(s):  
Anatoly Verlan ◽  
Volodymyr Fedorchuk
Keyword(s):  
Quality Control ◽  
Optimization Problems ◽  
Control Object ◽  
Optimality Criteria ◽  
Integrated Systems ◽  
Reference Solution ◽  
Computational Optimization ◽  
Control Signals ◽  
Modeling Accuracy ◽  
Solving Equations

For quality control in computer-integrated systems, it is assumed that the calculation of control signals is based on mathematical models of control objects. When solving the equations of the dynamics of the control object, it is necessary to take into account the limited computing resources of computer-integrated systems, which requires the choice of an effective method of solving equations, provided that the required accuracy of calculations. The paper considers a method for solving computational optimization problems in computer-integrated systems based on the proposed optimality criteria. A method is proposed based on the estimation of the discrepancy between the obtained and the reference solution to estimate the global error. The solution is accepted, the accuracy of which is two orders of magnitude higher than the required modeling accuracy.

scholarly journals Continuous Dynamics Related to Monotone Inclusions and Non-Smooth Optimization Problems

2020 ◽  
Vol 28 (4) ◽  
pp. 611-642 ◽  
Author(s):  
Ernö Robert Csetnek
Keyword(s):  
Dynamical Systems ◽  
Convex Optimization ◽  
Optimization Problems ◽  
Decisive Role ◽  
Energy Functional ◽  
Lyapunov Theory ◽  
Smooth Functions ◽  
Monotone Inclusions ◽  
Convex Optimization Problems ◽  
Smooth Optimization

Abstract The aim of this survey is to present the main important techniques and tools from variational analysis used for first and second order dynamical systems of implicit type for solving monotone inclusions and non-smooth optimization problems. The differential equations are expressed by means of the resolvent (in case of a maximally monotone set valued operator) or the proximal operator for non-smooth functions. The asymptotic analysis of the trajectories generated relies on Lyapunov theory, where the appropriate energy functional plays a decisive role. While the most part of the paper is related to monotone inclusions and convex optimization problems in the variational case, we present also results for dynamical systems for solving non-convex optimization problems, where the Kurdyka-Łojasiewicz property is used.

Numerical Techniques for Nonlinear Lagrangian Dynamical Systems and Their Application

2012 ◽  
Vol 476-478 ◽  
pp. 1513-1516
Author(s):  
Jin Li
Keyword(s):  
Dynamical Systems ◽  
General Framework ◽  
Optimization Problems ◽  
Lagrangian Function ◽  
Lagrangian System ◽  
Numerical Techniques ◽  
Constrained Optimization Problems ◽  
First Order ◽  
Nonlinear Lagrangian ◽  
Special Case

We provide a general framework for solving constrained optimization problems, this framework relies on dynamical systems using a class of nonlinear Lagrangian function, we construct a first order derivatives based and a second order derivatives based differential systems. Under this framework, We show that the exponential Lagrangian system as the special case is discussed.

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