323 research outputs found
The Geometry of Monotone Operator Splitting Methods
We propose a geometric framework to describe and analyze a wide array of
operator splitting methods for solving monotone inclusion problems. The initial
inclusion problem, which typically involves several operators combined through
monotonicity-preserving operations, is seldom solvable in its original form. We
embed it in an auxiliary space, where it is associated with a surrogate
monotone inclusion problem with a more tractable structure and which allows for
easy recovery of solutions to the initial problem. The surrogate problem is
solved by successive projections onto half-spaces containing its solution set.
The outer approximation half-spaces are constructed by using the individual
operators present in the model separately. This geometric framework is shown to
encompass traditional methods as well as state-of-the-art asynchronous
block-iterative algorithms, and its flexible structure provides a pattern to
design new ones
Axion Cosmology
1. Introduction 2. Models: the QCD axion; the strong CP problem; PQWW, KSVZ,
DFSZ; anomalies, instantons and the potential; couplings; axions in string
theory 3. Production and I.C.'s: SSB and non-perturbative physics; the axion
field during inflation and PQ SSB; cosmological populations - decay of parent,
topological defects, thermal production, vacuum realignment 4. The Cosmological
Field: action; background evolution; misalignment for QCD axion and ALPs;
cosmological perturbation theory - i.c.'s, early time treatment, axion sound
speed and Jeans scale, transfer functions and WDM; the Schrodinger picture;
simualting axions; BEC 5. CMB and LSS: Primary anisotropies; matter power;
combined constraints; Isocurvature and inflation 6. Galaxy Formation; halo mass
function; high-z and the EOR; density profiles; the CDM small-scale crises 7.
Accelerated expansion: the c.c. problem; axion inflation (natural and
monodromy) 8. Gravitational interactions with black holes and pulsars 9.
Non-gravitational interactions: stellar astrophysics; LSW; vacuum
birefringence; axion forces; direct detection with ADMX and CASPEr; Axion
decays; dark radiation; astrophysical magnetic fields; cosmological
birefringence 10. Conclusions A Theta vacua of gauge theories B EFT for
cosmologists C Friedmann equations D Cosmological fluids E Bayes Theorem and
priors F Degeneracies and sampling G Sheth-Tormen HMFComment: v2 greatly extended: 111 pages, 38 figures. Accepted for publication
in Physics Report
Advances in Energy System Optimization
The papers presented in this open access book address diverse challenges in decarbonizing energy systems, ranging from operational to investment planning problems, from market economics to technical and environmental considerations, from distribution grids to transmission grids, and from theoretical considerations to data provision concerns and applied case studies. While most papers have a clear methodological focus, they address policy-relevant questions at the same time. The target audience therefore includes academics and experts in industry as well as policy makers, who are interested in state-of-the-art quantitative modelling of policy relevant problems in energy systems. The 2nd International Symposium on Energy System Optimization (ISESO 2018) was held at the Karlsruhe Institute of Technology (KIT) under the symposium theme “Bridging the Gap Between Mathematical Modelling and Policy Support” on October 10th and 11th 2018. ISESO 2018 was organized by the KIT, the Heidelberg Institute for Theoretical Studies (HITS), the Heidelberg University, the German Aerospace Center and the University of Stuttgart
Penalty methods for the solution of generalized Nash equilibrium problems and hemivariational inequalities with VI constraints
In this thesis we propose penalty methods for the solution of Generalized Nash Equilibrium Problems (GNEPs) and we consider centralized and distributed algorithms for the solution of Hemivariational Inequalities (HVIs) where the feasible set is given by the intersection of a closed convex set with the solution set of a lower-level monotone Variational Inequality (VI)
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