In this course we discuss nonsmooth optimization problems arising in various areas of science and engineering. We develop the optimization theory and algorithms for a general class of variational problems. Applications are presented and analyzed for various examples inlcuding control and design optimization, inverse problem, image analysis and variational problems. Non-convex and non-smooth optimization becomes increasingly important for the advanced and effective use of optimization methods and thus theory are essential tools for mathematical modeling and analysis, We introduce basic function space and functional analysis tools need for the course.
The course provides an introduction to functional spaces and convex analysis and their basic concepts with illustrated examples. A general class of constrained optimization problems in function spaces is discussed and we develop the Lagrange multiplier theory and effective solution algorithms, Emerging applications of nonsmooth optimization include the image analysis, the classification and machine learning, the Bayesian statistics, and the mean-field analysis. We apply the optimization theory to analyze sparsity optimization and non-convex optimization and constrained PDE optimization problems and to treat such applications. Thus, the course provides the basic materials for nonsmooth optimization as well as how the theory and algorithms are put to use for advanced applications.
We are organizing an online conference on "Recent Progress in Nonlocal Modeling, Analysis, and Computation,” June 14 - 18, 2020. This conference is supported by the Department of Mathematics & SUSTech International Center for Mathematics at Southern University of Science and Technology, and Tianyuan Mathematical Center in Southeast China. The purpose is to bring together leading experts from different areas to showcase recent progress and discuss future challenges in the field of nonlocal problems.
Do you want to discover what your mathematics future could look like? Are you keen to meet and network with your mathematical peers? Then you can do so with the IMA! Come along to the 2020 Early Career Mathematicians' Autumn Conference on Saturday 24th October at the School of Mathematics and Statistics of the University of Glasgow.
Submissions are welcome on all areas of mathematics and its applications, as well as correlated subjects (which may include, but are not limited to, the history of mathematics, diversity and social activism in science, etc). Submissions are welcome from mathematicians early in their career, in academia and industry, students and educators of mathematical sciences, as well as from those with an interest in the subject. Submissions must be uploaded via https://my.ima.org.uk at the time of registration. All submissions are subject to rigorous review before an acceptance decision is made. The deadline for submission is 31 July 2020.
If you have any questions, please do not hesitate to contact the ECM Committee at email@example.com.
Electronic band energy of a bent ZnO piezoelectric semiconductor nanowire Wanli YANG, Yuantai HU, E. N. PAN
A full-coupling model of PN junctions based on the global-domain carrier motions with inclusion of the two metal/semiconductor contacts at endpoints Wanli YANG, Jinxi LIU, Yongliang XU, Yuantai HU
Vibration analysis of piezoelectric sandwich nanobeam with flexoelectricity based on nonlocal strain gradient theory Shan ZENG, Kaifa WANG, Baolin WANG, Jinwu WU
Jacobian-free Newton-Krylov subspace method with wavelet-based preconditioner for analysis of transient elastohydrodynamic lubrication problems with surface asperities N. M. BUJURKE, M. H. KANTLI
Interaction between a screw dislocation and an elliptical hole with two asymmetrical cracks in a one-dimensional hexagonal quasicrystal with piezoelectric effect Lianhe LI, Xiaowei CUI, Junhong GUO
Thomson and rotation effects during photothermal excitation process in magnetic semiconductor medium using variable thermal conductivity K. LOTFY, A. K. KHAMIS, A. A. EL-BARY, M. H. AHMED
Analysis of thermal responses in a two-dimensional porous medium caused by pulse heat flux T. SAEED, I. A. ABBAS
Design and fluid-structure interaction analysis for a microfluidic T-junction with chemo-responsive hydrogel valves E. KHANJANI, A. HAJARIAN, A. KARGAR-ESTAHBANATY, N. ARBABI, A. TAHERI, M. BAGHANI
Assessment of force models on finite-sized particles at finite Reynolds numbers Ruyang LI, Weixi HUANG, Lihao ZHAO, Chunxiao XU
A highly-efficient method for stationary response of multi-degree-of-freedom nonlinear stochastic systems Lincong CHEN, J. Q. SUN
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