Registered Data
Contents
- 1 [CT067]
- 1.1 [00542] Approximations of quasi-linear elliptic optimal control problems under variational and virtual discretizations
- 1.2 [00091] An infeasible interior-point arc-search algorithm for nonlinear constrained optimization
- 1.3 [00790] Machine learning methods with error analysis for optimal control problems
- 1.4 [00169] Decentralized strategies for coupled shape and parameter inverse problems
- 1.5 [01870] Point in a Polyhedron: A Computational Approach
[CT067]
[00542] Approximations of quasi-linear elliptic optimal control problems under variational and virtual discretizations
- Session Date & Time : 5D (Aug.25, 15:30-17:10)
- Type : Contributed Talk
- Abstract : This talk will discuss virtual and variational discretizations for the numerical approximation of optimal control problems governed by the quasi-linear elliptic equation with distributed control. A conforming virtual element method is employed for the discretization of state and co-state equations that appeared in the model problem. The numerical approximation of the control variable is based on two different discretizations: variational and virtual. In the variational approach, the discrete space associated with the control is not discretized explicitly, whereas, for the virtual discretizations, the discrete spaces are taken as virtual element spaces that include linear polynomials and non-polynomials functions over the polygonal mesh, and a discretize-then-optimize approach is used for the computation of control. With the help of certain projection operators, optimal a priori error estimates are established for the control, state, and co-state variables in suitable norms. Numerical experiments are presented under general polygonal meshes to illustrate the performance of the proposed scheme and verify the theoretical convergence rate.
- Classification : 49M29, 49M41, 65K15, 90C46
- Author(s) :
- Anil Kumar (BITS Pilani KK Birla Goa Campus, Goa (India))
- Jai Tushar (BITS Pilani KK Birla Goa Campus, Goa (India))
- Sarvesh Kumar (ndian Institute of Space Science and Technology, Thiruvananthapuram)
[00091] An infeasible interior-point arc-search algorithm for nonlinear constrained optimization
- Session Date & Time : 5D (Aug.25, 15:30-17:10)
- Type : Contributed Talk
- Abstract : Most algorithms based on interior-point methods are categorized as line search since they compute a search direction on a straight line. In this talk, we propose an interior-point method for nonlinear programming problems that computes the search direction along with an ellipsoidal arc. We discuss the convergence of the proposed method, and numerical experiments indicate it can solve the CUTEst benchmark problems in fewer iterations. A modified method can further reduce the computation time.
- Classification : 49M37, 65K05, 90C30, 90C51
- Author(s) :
- Einosuke Iida (Tokyo Institute of Technology)
- Makoto Yamashita (Tokyo Institute of Technology)
- Yaguang Yang (US NRC)
[00790] Machine learning methods with error analysis for optimal control problems
- Session Date & Time : 5D (Aug.25, 15:30-17:10)
- Type : Contributed Talk
- Abstract : We consider optimal control with partial differential equations (()PDE()) and present a numerical method based on machine learning including control error analysis. Physics-Informed Neural Networks (()PINN()) are used with the cost and penalty terms for the PDE as loss function. The model size is iteratively increased until the a posteriori estimated control error satisfies a given accuracy. The method is illustrated with numerical examples for 1D heat transfer and 3D turbine activation.
- Classification : 49M41, 49M25, 68T05, 65G20
- Author(s) :
- Georg Vossen (Kreleld University of Applied Sciences)
- Semih Sirin (Kreleld University of Applied Sciences)
- Nicolai Friedlich (Kreleld University of Applied Sciences)
[00169] Decentralized strategies for coupled shape and parameter inverse problems
- Session Date & Time : 5D (Aug.25, 15:30-17:10)
- Type : Contributed Talk
- Abstract : We present a novel family of algorithms framed within game theory setting and dedicated to solve ill-posed inverse problems, where unknown shapes (obstacles or inclusions) or sources are to be reconstructed as well as missing boundary conditions, for steady Stokes fluids. Some theoretical results and several numerical experiments are provided that corroborate the ability of the approch to tackle harsh problems.
- Classification : 49Mxx, 91Axx, 35Qxx
- Author(s) :
- Abderrahmane HABBAL (University Cote d'Azur Inria CNRS)
[01870] Point in a Polyhedron: A Computational Approach
- Session Date & Time : 5D (Aug.25, 15:30-17:10)
- Type : Contributed Talk
- Abstract : Determining whether a point is contained in a polyhedron or not has been revisited many times in history as it is one of the fundamental problems in computational geometry with immense application in three-dimensional CAD/CAM problems, in GIS (Geographic Information System). We at first review what has been done before and introduce methods based on computational techniques. We shall incorporate convex-hull techniques like Wang’s algorithm and provide method using Dehn’s invariant in three-dimensional Euclidean space. We shall also use Turaev-Viro invariance method and apply the algorithm to check point containment in a polyhedron. We are actually incorporating invariants (Dehn and Taurev-Viro) and the reason is two-fold. Firstly, using invariants like above we can distinguish between two polyhedrons and the second reason behind this is that both the invariants are suitable for computer algorithms.
- Classification : 51N20, 52B05, 52B10
- Author(s) :
- ARINDAM BHATTACHARYYA (JADAVPUR UNIVERSITY)