# Registered Data

## [02404] New Trends in Hierarchical Variational Inequalities and Optimization Problems

**Session Date & Time**:- 02404 (1/4) : 1C (Aug.21, 13:20-15:00)
- 02404 (2/4) : 1D (Aug.21, 15:30-17:10)
- 02404 (3/4) : 1E (Aug.21, 17:40-19:20)
- 02404 (4/4) : 2C (Aug.22, 13:20-15:00)

**Type**: Proposal of Minisymposium**Abstract**: It is well known that the bilevel programming problem has been widely investigated in the literature due to its applications in mechanics, network designs and so on. In particular, if the upper-level problem is a variational inequality problem and the lower-level is a fixed-point set of an operator, then such a bilevel problem is known as a hierarchical variational inequality problem. The signal recovery, beamforming and power control problems can be modelled as hierarchical variational inequality problems. This minisymposium will promote a few scholars to look into new trends in hierarchical variational inequalities and optimization problems together, and provide an opportunity to explore the latest developments.**Organizer(s)**: Lu-Chuan Ceng**Classification**:__65K15__,__47H05__,__47H10__,__65Y05__,__68W25__**Speakers Info**:**Lu-Chuan Ceng**(Shanghai Normal University)- Yun-Ling Cui (Shanghai Normal University)
- Yun-Shui Liang (Yichun Vocational Technique College)
- Hui-Ying Hu (Shanghai Normal University)
- Yang-Qing Qiu (Shanghai Polytechnic University)

**Talks in Minisymposium**:**[03031] Self-adaptive subgradient extragradient method with extrapolation procedure for MSVIs****Author(s)**:**Lu-Chuan Ceng**(Shanghai Normal University)

**Abstract**: This article introduces a self-adaptive subgradient extragradient process with extrapolation to solve a bilevel split pseudomonotone variational inequality with common fixed points constraint of finite nonexpansive mappings. The proposed rule exploits the strong monotonicity of one operator at the upper level and the pseudomonotonicity of another mapping at the lower level. The strong convergence result for the proposed algorithm is established. A numerical example is used to demonstrate the viability of the proposed rule.

**[03050] Subgradient-extragradient method for SEP, VIP and FPP of multi-valued mapping****Author(s)**:**Yun-shui Liang**(Yichun Vocational Technique College)

**Abstract**: In this paper, via a subgradient extragradient implicit rule, we introduce a new iterative algroithm for solving split equilibrium problems, variational inequality problem and fixed point problem of nonspreading multi-valued mapping in Hilbert space. We show that the iteration converges strongly to a common solution of the considered problems. Our results extend and improve some well-known results in the literature. Finally, a numerical example is provided to verify the validity of the proposed algorithm.

**[03061] Modified subgradient-extragradient method for monotone-bilevel-equilibria with VIP and CFPP constraints****Author(s)**:**Hui-ying Hu**(shanghai normal university)

**Abstract**: In a real Hilbert space, let GSVI and CFPP represent a general system of variational inequalities and a common fixed point problem of a countable family of nonexpansive mappings and an asymptotically nonexpansive mapping, respectively. In this paper, we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP constraints. Some strong convergence results for the proposed algorithms are established under the mild assumptions.

**[03072] New strong convergence theorems of generalized quasi-contractive mappings****Author(s)**:**Yangqing Qiu**(Shanghai Polytechnic University)

**Abstract**: In this paper, the strong convergences and estimates of convergence rate for generalized quasi-contractive mappings and generalized set-valued quasi-contractive mappings are studied in a real Hilbert space. Firstly, the Picard iterative process is used to approximate the fixed point. Secondly, a characterization of strong convergence theorem of the Mann iterative sequence is proved. By virtue of the mean value theorem of integrals, the convergence rate and the error estimate of the iterative processes are given.

**[03144] Mittag-leffler stability of Fractional-order Neural Networks with time-varying delays****Author(s)**:**wei ding**- xiang zhu (Shanghai Normal University)

**Abstract**: This paper mainly studies a kind of fractional-order neural networks with time-varying delays. By using the mean value theorem of integrals, inequality technique and Banach fixed point theorem, the Mittag-leffler stability of the unique equilibrium point of the system can be proved when some satisfied conditions are built.

**[03170] Singular Riemann problems and their applications****Author(s)**:**Aifang Qu**(Shanghai Normal University)

**Abstract**: In this talk, we will focus on a class of singular Riemann problems which contain concentration supported at the initial discontinuity. It corresponds to the study of a class of measure partial differential equations. Further, we will briefly introduce some applications of these problems to the study of hypersonic limit flow passing a wedge, fluid-structure interaction problems and conservation laws with discontinuous flux.

**[03270] Gas-liquid Phase Transition Problem for Non-isentropic Compressible Euler Equations****Author(s)**:**Pei-yu Zhang**(Shanghai Normal University)

**Abstract**: We study gas-liquid phase transition problem described by one-dimensional non-isentropic Euler equations. For this purpose, we solve the Riemann problem for non-isentropic Euler equations in the class of Radon measure. The difficulty is to find a meaningful solution to Riemann problem that satisfies the occurrence of this gas-liquid phase transformation phenomenon. This provide a new way of thinking for the study of gas-liquid phase transition.

**[03286] Accelerated subgradient-extragradient methods for VIPs and CFPPs implicating countable nonexpansive-operators****Author(s)**:**Yun-ling Cui**(shanghai normal university)

**Abstract**: In a real Hilbert space, let the VIP and CFPP denote the variational inequality problem and common fixed-point problem of countable nonexpansive operators and asymptotically nonexpansive operator, respectively. In this paper, we construct two modified Mann-type subgradient extragradient rules with a linear-search process for finding a common solution of the VIP and CFPP. We demonstrate the strong convergence of the suggested rules to a common solution of the VIP and CFPP.

**[03591] The Behaviors of Rupture Solutions for a Class of Elliptic MEMS Equations****Author(s)**:**Yanyan Zhang**(East China Normal University)

**Abstract**: We will talk about the rupture solutions of a semilinear elliptic equation $$\Delta u=\frac{\lambda |x|^{\alpha}}{u^p},\quad x\in\mathbb{R}^2\backslash\{0\},u(0)=0,\lambda>0,p>0,\alpha>-2,$$ which derived from fields such as Micro-Electro-Mechanical System(MEMS). The remarkable feature of MEMS equations is the singularity of nonlinear terms. In this talk, we will firstly analysis the classification of all possible singularities at $x=0$ for rupture solutions $u(x)$. In particular, we show that for some $(\alpha,p)$, $u(x)$ admits only the isotropic singularity at $x=0$, and otherwise $u(x)$ may admit the anisotropic singularity at $x=0$. Secondly, global solutions in $\mathbb{R}^2\backslash\{0\}$(their existence and their behavior near $x=\infty$ as well as near $x=0$) are also studied. These results contribute to providing theoretical basis for the design and application of MEMS devices. This is a joint work with Y.J. Guo, F. Zhou and Qing Li.