GRAPH-STRUCTURED TENSOR OPTIMIZATION FOR NONLINEAR DENSITY CONTROL AND MEAN FIELD GAMES

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This thesis focuses on the development of advanced algorithmic techniques, primarily Markov Chain Monte Carlo (MCMC) methods, and message passing algorithms, to tackle high-dimensional optimization and inference problems. The algorithms used have a probabi ...

Partial differential equations can model diverse physical phenomena including heat diffusion, incompressible flows, and electrostatic potentials. Given a description of an object's boundary and interior, traditional methods solve such PDEs by densely meshi ...

We study a transportation problem where two heavy-duty trucks travel across the national highway from separate origins to destinations, subject to individual deadline constraints. Our objective is to minimize their total fuel consumption by jointly optimiz ...

The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization solvers near global ...

Although Lipschitz-constrained neural networks have many applications in machine learning, the design and training of expressive Lipschitz-constrained networks is very challenging. Since the popular rectified linear-unit networks have provable disadvantage ...

Many approximate solutions of the time-dependent Schrodinger equation can be formulated as exact solutions of a nonlinear Schrodinger equation with an effective Hamiltonian operator depending on the state of the system. We show that Heller's thawed Gaussia ...

Multi-energy microgrid (MEMG) has the potential to improve the energy utilization efficiency. However, the uncertainty caused by distributed renewable energy resources brings an urgent need for multi-energy co -optimization to ensure secure operation. This ...

In this paper we present a mathematical and numerical model for human cardiac perfusion which accounts for the different length scales of the vessels in the coronary tree. Epicardial vessels are represented with fully three-dimensional (3D) fluid-dynamics, ...

Part I of this paper formulated a multitask optimization problem where agents in the network have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness condition over the graph. A diffusion strategy was devised ...

Polarization-adjusted convolutional (PAC) codes are modified polar codes in which a one-to-one convolutional transformation is employed before the classical polar transform. Fano decoding of PAC codes in the Shannon lecture at ISIT2019 showed an outstandin ...

GRAPH-STRUCTURED TENSOR OPTIMIZATION FOR NONLINEAR DENSITY CONTROL AND MEAN FIELD GAMES

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