Численные методы оптимизации для задач большой размерности: неточный оракул и прямо-двойственный анализ Двуреченский Павел Евгеньевич

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Двуреченский, Павел Евгеньевич.
Численные методы оптимизации для задач большой размерности: неточный оракул и прямо-двойственный анализ = Numerical methods in large-scale optimization: inexact oracle and primal-dual analysis : Numerical methods in large-scale optimization: inexact oracle and primal-dual analysis : диссертация ... доктора физико-математических наук : 01.01.09 / Dvurechenskii Pavel Evgenievich ; [Место защиты: ФГАОУ ВО «Московский физико-технический институт (национальный исследовательский университет)»]. - Москва, 2020. - 274 с. : ил.
Оглавление диссертациидоктор наук Двуреченский Павел Евгеньевич
Contents
1 Introduction
2 Optimization with inexact oracle
2.1 Stochastic intermediate gradient method for convex problems with stochastic inexact oracle
2.2 Learning supervised pagerank with gradient-based and gradient-free optimization methods
2.2.1 Loss-minimization problem statement
2.2.2 Solving the learning problem by zero-order method
2.2.3 Solving the learning problem by first-order method
2.3 An accelerated directional derivative method for smooth stochastic convex optimization
2.3.1 Algorithms and main results for convex problems
2.3.2 Algorithms and main results for strongly convex problems
3 Primal-dual methods
3.1 Primal-dual methods for solving infinite-dimensional games
3.1.1 Algorithm for convex-concave problem
3.1.2 Algorithm for strongly convex-concave problem
3.2 Accelerated primal-dual gradient method for strongly convex problems with linear constraints
3.3 Distributed primal-dual accelerated stochastic gradient method
3.4 Primal-dual accelerated gradient method with small-dimensional relaxation oracle
4 Conclusion
5 References
6 Appendix
A Paper "Stochastic intermediate gradient method for convex problems with stochastic inexact oracle"
B Paper "Stochastic intermediate gradient method for convex optimization problems"
C Paper "Learning supervised pagerank with gradient-based and gradientfree optimization methods"
D Paper "An accelerated directional derivative method for smooth stochastic convex optimization"
E Paper "Primal-dual methods for solving infinite-dimensional games"
F Paper "Fast primal-dual gradient method for strongly convex minimization problems with linear constraints"
G Paper "Computational optimal transport: Complexity by accelerated gradient descent is better than by Sinkhorn's algorithm"
H Paper "Decentralize and randomize: Faster algorithm for Wasserstein barycenters"
I Paper "Accelerated primal-dual gradient descent with linesearch for convex, nonconvex, and nonsmooth optimization problems"
J Paper "Primal-dual accelerated gradient methods with small-dimensional relaxation oracle"