On Certain Hypotheses in Optimal Control Theory and the Relationship of the Maximum Principle with the Dynamic Programming Method Proposed by L. I. Rozonoer

数学规划与均衡约束（MPECs）优化研讨会笔记：MPEC假设的验证

Optimization Workshop Notes for Mathematical Programming with Equilibrium Constraints (MPECs): Verification of MPEC Hypotheses

本文介绍非线性规划、变分不等式和互补系统的基本语言，探讨MPEC最优性条件成立的数学逻辑，并指导如何在研究中应用该理论进行模型分类和假设验证。

Bounded-From-Below Solutions of the Hamilton-Jacobi Equation for Optimal Control Problems with Exit Times: Vanishing Lagrangians, Eikonal Equations, and Shape-From-Shading

We study the Hamilton-Jacobi equation for undiscounted exit time control problems with general nonnegative Lagrangians using the dynamic programming approach. We prove theorems characterizing the value function as the unique bounded-from-below viscosity solution of the Hamilton-Jacobi equation which is null on the target. The result applies to problems with the property that all trajectories satisfying a certain integral condition must stay in a bounded set. We allow problems for which the Lagrangian is not uniformly bounded below by positive constants, in which the hypotheses of the known uni…

LQG平均场博弈中基于均值场轨迹的成本与控制逆问题

Inverse Problems for Costs and Controls in LQG MFGs via Mean Field Trajectories

研究基于均值-协方差轨迹观测的LQG平均场博弈逆问题，提出半定规划方法推断与观测动力学一致的成本参数。

McKean-Vlasov随机微分方程的无限时间最优控制

Infinite Time Horizon Optimal Control of McKean-Vlasov SDEs

本文提出无限时间折扣McKean-Vlasov随机微分方程最优控制理论，证明值函数的时间不变性及其对初始分布的二阶Wasserstein空间依赖性，建立动态规划原理并推导椭圆HJB方程的粘性解唯一性。

Active sequential hypothesis testing

Consider a decision maker who is responsible to dynamically collect observations so as to enhance his information about an underlying phenomena of interest in a speedy manner while accounting for the penalty of wrong declaration. Due to the sequential nature of the problem, the decision maker relies on his current information state to adaptively select the most ``informative'' sensing action among the available ones. In this paper, using results in dynamic programming, lower bounds for the optimal total cost are established. The lower bounds characterize the fundamental limits on the maximum a…