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[CT066]

CT066 (1/1) : Existence theories in calculus of variations and optimal control (49J) / Hamilton-Jacobi theories (49L) / Real and complex geometry (51M) / Variational methods for eigenvalues of operators (49R)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @F401
Type : Contributed Talk
Abstract : In this talk, the stability of solutions to parametric split equality and split feasibility problems is addressed for the first time. Characterizations for the Lipschitz-likeness of solution maps are obtained by exploiting special structures of the problems and by using an advanced result of B.S. Mordukhovich on parametric generalized equations. Examples are presented to illustrate how the obtained results work in practice and to show that extra mild assumptions made cannot be omitted.
Classification : 49J53, 49K40, 65K10, 90C25, 90C31
Format : Talk at Waseda University
Author(s) :
- Huong Thi Vu (Institute of Mathematics, Vietnam Academy of Science and Technology)
- Yen Dong Nguyen (Institute of Mathematics, Vietnam Academy of Science and Technology)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @F401
Type : Contributed Talk
Abstract : Developing efficient algorithms for Hamilton--Jacobi partial differential equations $(\text{HJ PDEs})$ is crucial for solving high-dimensional optimal control problems in real time but notoriously tricky due to the so-called curse of dimensionality. In this talk, we present novel grid-free and embarrassingly-parallel optimization algorithms for solving a broad class of HJ PDEs relevant to high-dimensional state-dependent optimal control problems. We illustrate their performance and efficiency on large-scale multi-agent path planning problems.
Classification : 49L12, 65K10, 90C30, 49M29, 49M37
Format : Talk at Waseda University
Author(s) :
- Gabriel Provencher Langlois (New York University)
- Jerome Darbon (Brown University)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @F401
Type : Contributed Talk
Abstract : Cartograms are maps in which the areas of enumeration units $\text{(}$e.g. administrative divisions$\text{)}$ are proportional to quantitative data $\text{(}$e.g. population$\text{)}$. Generating cartograms with density-equalising map projections guarantees that geographic neighbours remain neighbours in the cartograms if all boundaries are infinitely dense sequences of points. However, computers represent boundaries with only finitely many points, often causing invalid topologies in the cartogram. This talk shows how line densification and topology-aware simplification solve this problem.
Classification : 51M30, 53-08, 68-04
Format : Talk at Waseda University
Author(s) :
- Michael T Gastner (Yale-NUS College)
- Nguyen Phong Le (Yale-NUS College)
- Nihal Z Miaji (Yale-NUS College)
- Adi Singhania (Yale-NUS College)

Session Time & Room : 2E (Aug.22, 17:40-19:20) @F401
Type : Contributed Talk
Abstract : This paper discusses three numerical schemes for Generalized Isoperimetric Constraint Fractional Variational Problems (GICFVPs) defined using generalized fractional derivatives. Three Numerical schemes, i.e. linear, quadratic, and quadratic-linear schemes, are used to get numerical solutions of a GICFVP. The convergence rate of the linear and quadratic schemes for $\alpha\in(0,1)$ are $2-\alpha$ and $3-\alpha$. It is observed that the presented schemes perform well, and when the step size $\mathrm{h}$ is decreased, the desired solution is attained.
Classification : 49R99, 65K10, 65L60, 65L70
Format : Online Talk on Zoom
Author(s) :
- DIVYANSH PANDEY (IIT (BHU), Varanasi)
- Rajesh Kumar Pandey (IIT (BHU), Varanasi)