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Lecturer(s)
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Hron Karel, prof. RNDr. Ph.D.
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Course content
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Optimization 1. Methods for solving one-dimensional minimization problems. 2. Minimization methods for nondifferentiable multivariable functions. 3. Gradient methods for quadratic functions. 4. Gradient methods for general functions. 5. Newton's method and quasi-Newton methods. 6. Step length in descent methods. 7. Optimality conditions for nonlinear programming problems 8. Lagrangian function and duality. 9. Quadratic programming. 10. Nonlinear programming with linear constrains. 11. Penalty methods. 12. Augmented Lagrangian method. Methods of approximation 1. Spline definition and representation. 2. B-splines and their properties. 3. Spline interpolation. 4. Splines in the least square problem. 5. Smoothing splines 6. Tensor product splines and application.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Realize contexture of basic conceptions and statements concerning optimization and methods of approximation.
Synthesis Realize contexture of basic conceptions and statements concerning the course content.
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Prerequisites
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The student has to meet all prerequisites given for the study course Applied Mathematics and all the conditions of Study and Examination Regulations of the Palacký University in Olomouc.
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Assessment methods and criteria
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unspecified
The student has to understand the subject.
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Recommended literature
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