Inexact Model: A Framework for Optimization and Variational Inequalities

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many known methods as a special case, the list including accelerated gradient method, composite optimization methods, level-set methods, proximal methods. The idea of the framework is based on constructing an inexact model of the main problem component, i.e. objective function in optimization or operator in variational inequalities. Besides reproducing known results, our framework allows to construct new methods, which we illustrate by constructing a universal method for variational inequalities with composite structure. This method works for smooth and non-smooth problems with optimal complexity without a priori knowledge of the problem smoothness. We also generalize our framework for strongly convex objectives and strongly monotone variational inequalities.Comment: 41 page

The Electron-Proton Bound State in the Continuum with the Positive Binding Energy of 1.531 of the Electron Mass

In the bound states in the continuum (BIC), the binding energy is positive, and the mass of a composite particle is greater than the total mass of its constituents. In this work, the BIC state is studied for the electron-proton system using the ladder Bethe-Salpeter equation. We demonstrate that there is a momentum space region in which the electromagnetic interaction between the particles is strongly enhanced, and the effective coupling constant is α p mp/me = 0.313, where α is the fine structure constant, and mp and me are the proton and the electron masses. This interaction resonance causes the confinement of the pair in the BIC state with the positive binding energy of 1.531me. The integral equation for the bispinor wave function is derived. This normalized wave function, which must be complex, was found numerically. It turned out that in the BIC state, the average radius for the electron is 48 Fm, and that for the proton is 1.1 Fm. This composite boson can exist exclusively in the free state, in which its properties, such as its form factors, should only be studied. In bound states with other particles, the composite loses its individuality. In Stern-Gerlach experiments, the electron-proton composite boson will demonstrate the properties of a spin 1/2 fermion

Work Extraction and Landauer's Principle in a Quantum Spin Hall Device

Landauer's principle states that erasure of each bit of information in a system requires at least a unit of energy $k_B T \ln 2$ to be dissipated. In return, the blank bit may possibly be utilized to extract usable work of the amount $k_B T \ln 2$, in keeping with the second law of thermodynamics. While in principle any collection of spins can be utilized as information storage, work extraction by utilizing this resource in principle requires specialized engines that are capable of using this resource. In this work, we focus on heat and charge transport in a quantum spin Hall device in the presence of a spin bath. We show how a properly initialized nuclear spin subsystem can be used as a memory resource for a Maxwell's Demon to harvest available heat energy from the reservoirs to induce charge current that can power an external electrical load. We also show how to initialize the nuclear spin subsystem using applied bias currents which necessarily dissipate energy, hence demonstrating Landauer's principle. This provides an alternative method of "energy storage" in an all-electrical device. We finally propose a realistic setup to experimentally observe a Landauer erasure/work extraction cycle.Comment: Accepted for publication PRB, 9 pages, 4 figures, RevTe

Совместное управление сигналами светофоров и траекториями движения транспортных средств

Транспортная система является одной из важнейших частей экономики страны. В то же время, рост интенсивности транспортного потока оказывает существенное отрицательное влияние на экономические показатели отрасли. Одним из способов повышения эффективности использования транспортной инфраструктуры является управление транспортными потоками. Решение задачи эффективного управления транспортными потоками в настоящее время часто осуществляется путем применения систем управления сигналами светофоров на регулируемых перекрёстках. В связи с развитием и постепенным внедрением самоорганизующихся автомобильных сетей, позволяющих обмениваться информацией между транспортными средствами и объектами инфраструктуры, а также развитием автономных транспортных средств другим перспективным подходом к решению рассматриваемой задачи является управление траекторией движения беспилотных транспортных средств. Как следствие, становится возможной постановка задачи совместного управления траекториями движения транспортных средств и сигналами светофоров для повышения пропускной способности перекрестков, снижения потребляемого топлива и времени движения. В данной работе представлен метод управления транспортным потоком на перекрестке, заключающийся в совместном управлении сигналами светофоров и траекториями движения подключенных/автономных транспортных средств. Разработанный метод сочетает метод адаптивного управления сигналами светофоров, основанный на детерминированной модели прогнозирования движения транспортных средств, и двухэтапный алгоритм построения траектории движения транспортных средств. Целевая функция оптимизации, используемая для построения оптимальных траекторий, учитывает расход топлива, время движения по дорожной полосе и время ожидания на перекрестке. Экспериментальные исследования разработанного метода проведены в системе микроскопического моделирования движения транспортных средств SUMO с использованием трех сценариев моделирования, включающих синтетические сценарии и сценарий движения в реальной городской среде. Результаты экспериментальных исследований подтверждают эффективность разработанного метода по критериям потребления топлива, времени движения и времени ожидания по сравнению с методом адаптивного управления сигналами светофоров

Inexact model: A framework for optimization and variational inequalities

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many known methods as a special case, the list including accelerated gradient method, composite optimization methods, level-set methods, proximal methods. The idea of the framework is based on constructing an inexact model of the main problem component, i.e. objective function in optimization or operator in variational inequalities. Besides reproducing known results, our framework allows to construct new methods, which we illustrate by constructing a universal method for variational inequalities with composite structure. This method works for smooth and non-smooth problems with optimal complexity without a priori knowledge of the problem smoothness. We also generalize our framework for strongly convex objectives and strongly monotone variational inequalities

Inexact relative smoothness and strong convexity for optimization and variational inequalities by inexact model

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many known methods as a special case, the list including accelerated gradient method, composite optimization methods, level-set methods, Bregman proximal methods. The idea of the framework is based on constructing an inexact model of the main problem component, i.e. objective function in optimization or operator in variational inequalities. Besides reproducing known results, our framework allows to construct new methods, which we illustrate by constructing a universal conditional gradient method and universal method for variational inequalities with composite structure. These method works for smooth and non-smooth problems with optimal complexity without a priori knowledge of the problem smoothness. As a particular case of our general framework, we introduce relative smoothness for operators and propose an algorithm for VIs with such operator. We also generalize our framework for relatively strongly convex objectives and strongly monotone variational inequalities

Inexact relative smoothness and strong convexity for optimization and variational inequalities by inexact model

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many known methods as a special case, the list including accelerated gradient method, composite optimization methods, level-set methods, Bregman proximal methods. The idea of the framework is based on constructing an inexact model of the main problem component, i.e. objective function in optimization or operator in variational inequalities. Besides reproducing known results, our framework allows to construct new methods, which we illustrate by constructing a universal conditional gradient method and universal method for variational inequalities with composite structure. These method works for smooth and non-smooth problems with optimal complexity without a priori knowledge of the problem smoothness. As a particular case of our general framework, we introduce relative smoothness for operators and propose an algorithm for VIs with such operator. We also generalize our framework for relatively strongly convex objectives and strongly monotone variational inequalities