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This thesis addresses the problem of designing cost-efficient decentralized energy sup- ply networks, which allow for distributed forms of energy generation. Two major contri- butions are made: A novel mathematical modeling approach of designing decentralized energy supply networks is proposed and solution strategies, in particular, those which are based on linearization, are studied and extended for practically relevant mixed-integer non- linear optimization. We couple the energy supply of electricity and natural gas into one network and in- troduce mirco-energy-conversion technologies in order to meet the demand of heat and electricity for residential houses. A unifying modeling approach based on mixed-integer nonlinear programming is proposed, which models practical decisions, such as network expansion, technology distribution and energy-efficient house renovation, and takes into account the nonlinear physical law of energy flows. The complexity of the problem poses a considerably computational challenge. We exploit the particular structure of our problem formulation and develop tailored solution methods with linearization techniques. Both approximation and relaxation of non- convex functions are considered based on mixed-integer formulations of piecewise linear functions. Extensive computational studies are presented, showing their numerical perfor- mance for solving nonconvex MINLP problems. published

Many image processing tasks involve image-to-image mapping, which can be addressed well by fully convolutional networks (FCN) without any heavy preprocessing. Although empirically designing and training FCNs can achieve satisfactory results, reasons for the improvement in performance are slightly ambiguous. Our study is to make progress in understanding their generalization abilities through visualizing the optimization landscapes. The visualization of objective functions is obtained by choosing a solution and projecting its vicinity onto a 3D space. We compare three FCN-based networks (two existing models and a new proposed in this paper for comparison) on multiple datasets. It has been observed in practice that the connections from the pre-pooled feature maps to the post-upsampled can achieve better results. We investigate the cause and provide experiments to shows that the skip-layer connections in FCN can promote flat optimization landscape, which is well known to generalize better. Additionally, we explore the relationship between the models generalization ability and loss surface under different batch sizes. Results show that large-batch training makes the model converge to sharp minimizers with chaotic vicinities while small-batch method leads the model to flat minimizers with smooth and nearly convex regions. Our work may contribute to insights and analysis for designing and training FCNs., In AAAI-19 Workshop on Network Interpretability for Deep Learning

The project concerns with the mathematical modeling and global optimization of energy supply networks based on multiple-energy carriers for urban family houses. published

We consider an optimization problem of energy supply networks based on multiple-energy carriers for urban family houses by taking into account new energy supply concepts. Under the background of growing penetration of micro energy-cogeneration technologies, our goal is to design hybrid energy supply networks for providing electricity and heat, especially, we are interested in developing an optimal strat- egy to simultaneously determine the transmission lines of the underlying energy carriers as well as the distribution of micro energy technologies, which route the energy carrier flows. We propose a mixed-integer nonlinear programming (minlp) model to investigate the problem. However, due to its high complexity and large size of practical instances, it is challenging to compute optimal solutions. We apply piecewise linear ap- proximation techniques and specific convexification structures to improve the solution process based on the branch-and-bound method. Numerical tests based on simulated data are presented to demonstrate the capability of our approaches. published

Based on a clear analysis of the latest Windows driver framework WDF, this paper has implemented a driver of the PCIe-SpaceWire interface card device and put forward a discussion about ensuring the stability of PCIe driver. At the same time, Qt and OpenGL are used to design the upper application. Finally, a functional verification of the control software is provided., Comment: 4 pages, 13 figures

The paper deals with the option pricing problem in jump-diffusion models numerically. In the first part, the affine Galerkin method is applied to solve the implied pricing PIDE. In the second part, the POD method is applied to reduce the numerical complexity of the affine Galerkin scheme. Numerical results are presented.