# Registered Data

Contents

- 1 [CT066]
- 1.1 [00629] Stability Analysis of Split Equality and Split Feasibility Problems
- 1.2 [02374] Embarrassingly-parallel optimization algorithms for high-dimensional optimal control
- 1.3 [00567] Topology-aware algorithm for constructing cartograms from density-equalising map projections
- 1.4 [00238] Numerical Schemes for Generalized Isoperimetric Constraint Fractional Variational Problem

# [CT066]

**Session Time & Room****Classification**

## [00629] Stability Analysis of Split Equality and Split Feasibility Problems

**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)

## [02374] Embarrassingly-parallel optimization algorithms for high-dimensional optimal control

**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)

## [00567] Topology-aware algorithm for constructing cartograms from density-equalising map projections

**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)

## [00238] Numerical Schemes for Generalized Isoperimetric Constraint Fractional Variational Problem

**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)