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[CT064]

CT064 (1/1) : Optimality conditions (49K) / Miscellaneous applications of operator theory (47N)

Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
Type : Contributed Talk
Abstract : The paper discusses the exact bounds for the effective properties of multimaterial composites. We refine Hashin-Shtrikman bounds in the region where the last ones are loose. We show that fields in optimal structures vary in restricted domains, modify the Translation method, and obtain new exact bounds and optimal structures. Different volume fractions of components correspond to topologically different types of optimal structures.
Classification : 49K20
Format : Talk at Waseda University
Author(s) :
- Andrej Cherkaev (University of Utah)

Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
Type : Contributed Talk
Abstract : Doubly diffusive flows involve coupled incompressible flow and double diffusion transport, which models physical problems like bacteria bioconvection, exothermic flows in oceanography and more. We study a distributed optimal control problem governed by doubly diffusive flows under minimal regularity on 2D and 3D bounded Lipschitz domains and establish its well-posedness. First and second-order optimality conditions are derived. Furthermore, a discretization of the control problem based on $H(\mbox{div})$-conforming discontinuous Galerkin finite elements for the state and adjoint variables and piecewise constant finite elements for the control variable is discussed. Optimal apriori error estimates are proven in suitable norms. Numerical experiments are performed using a semi-smooth Newton strategy verifying the theoretical findings.
Classification : 49K20, 65N30, 76S05, 76R50, 49K27
Format : Talk at Waseda University
Author(s) :
- Jai Tushar (Indian Institute of Technology Roorkee)
- Arbaz Khan (IIT Roorkee)
- Manil T. Mohan ( IIT Roorkee)

Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
Type : Contributed Talk
Abstract : Decentralized optimization problems consist of multiple agents connected by a network. The agents have each local cost function, and the goal is to minimize the sum of the functions cooperatively. In this work, we propose a gradient-push algorithm involving event-triggered communication on a directed network. The convergence of the algorithm is established under suitable decays and summability conditions on a stepsize and triggering threshold.
Classification : 47Nxx, 65Kxx, Decentralized Optimization
Format : Talk at Waseda University
Author(s) :
- jimyeong kim (Sungkyunkwan University)
- Woocheol Choi (Sungkyunkwan Univeristiy)

Session Time & Room : 2C (Aug.22, 13:20-15:00) @F312
Type : Contributed Talk
Abstract : Strong metric subregularity and strong metric regularity of the natural residual and the normal map are of particular importance in the convergence analysis of first-order and second-order algorithms for composite-type optimization problems. In this talk, we characterize the strong metric subregularity of the natural residual and the normal map for a general class of nonsmooth nonconvex composite functions and establish the equivalence between these conditions, the strong metric subregularity of the subdifferential, and the quadratic growth condition. Furthermore, if the nonsmooth part of the objective function has a strictly decomposable structure, then strong metric regularity of the subdifferential is shown to be equivalent to strong metric regularity of natural residual and the normal map and to a counterpart of the so-called strong second-order sufficient conditions. Finally, we provide a link of these conditions to nonsingularity of the generalized Jacobians of the normal map and natural residual.
Classification : 47Nxx, 47Nxx, 47Nxx, 47Nxx, 47Nxx, Variational Analysis
Format : Online Talk on Zoom
Author(s) :
- Wenqing Ouyang (The Chinese University of HongKong(Shenzhen))
- Andre Manfred Milzarek (The Chinese University of Hong Kong, Shenzhen)