Computational Methods for Optimization of a Beam of Trajectories With a Non-smooth Quality Functional
Year: 2025
Type: article
Abstract: The problem of analyzing systems under conditions of deterministic uncertainty in the initial state of the system is related to the problems of practicalstability and optimization of trajectory bundles. For problems of parametric optimization of systems, one of the main approaches is to formulatestatements with criteria in the form of a maximum under initial conditions of the functional, which is analyzed on the solutions of the system. This, inturn, encourages the use of non-smooth optimization methods taking into account the presence of a parametric system and the development ofcomputational methods that are characteristic of such an area. In this case, the apparatus of generalized derivatives and generalized differentials isused, the computational methods are modifications of iterative procedures of the subgradient descent type in various modifications. It should be notedthat in such problems only in some cases can algorithms characteristic of convex cases be applied. The paper considers a problem with a qualitycriterion of the type of maximum under initial conditions of the terminal functional. The authors substantiate the theorem on the structure of thederivative in the direction, as well as the necessary conditions for the extremum. Based on the theoretical results, the method of the fastest descent isconstructed in the work. For the case of a linear system with a quadratic quality criterion, the method of coordinate descent and the method ofellipsoids are used. A computational experiment was conducted and the results of the calculations are presented. It should be noted that the applicationof the theoretical results given in the work and related to the methods of non-smooth optimization is complicated when performing practicalcalculations due to the complexity of the statements and, therefore, a significant number of calculations at each iteration, the convergence rate of suchmethods is quite moderate. Therefore, it is important, on the one hand, to develop numerical methods that could be implemented. For this, it isadvisable to use methods of qualitative analysis, in particular methods of practical stability, to estimate the set of scatter of initial conditions in theclass of ellipsoids, as well as the method of structural-parametric optimization of systems. On the other hand, it is necessary to evaluate qualitativecharacteristics such as initial approximation, step size, approximative properties, etc.
Institution: Taras Shevchenko National University of Kyiv
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415208517
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