8 papers · 1 filter
Bilinear control of age--space structured populations
Jiguang Yu, Louis Shuo Wang, Ye Liang
We study constrained bilinear optimal control for nonlocal age--space structured population equations with renewal boundary conditions and endogenous surveillance feedback. The con…
Nonsmooth Obstacles and Killed Resolvents in Reflected Stochastic Control
Louis Shuo Wang, Jiguang Yu
We study an infinite-horizon optimal stopping problem for a normally reflected two-dimensional diffusion in the quadrant with nonsmooth max-type payoff \(G(x_1,x_2)=x_1\veeαx_2\).…
First-Order Optimality Conditions for Mathematical Programming with Equilibrium Constraints
Louis Shuo Wang
We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical n…
Introduction to Exact Penalization for Mathematical Programming with Equilibrium Constraints
Louis Shuo Wang
We present a focused introduction to exact penalty methods for nonlinear programs and mathematical programs with equilibrium constraints (MPECs), emphasizing their connection to mo…
Introduction to Mathematical Programming with Equilibrium Constraints (MPECs) and Bilevel Optimization
Louis Shuo Wang
Our aim is to explain mathematical programs with equilibrium constraints (MPECs), motivate them through applications, present the main equivalent formulations of equilibrium constr…
Lecture Note for Bounded Controls in Continuous-Time and Control of Several Variables
Louis Shuo Wang
In this note, we develop the first-order theory of optimal control problems with box constraints on the control. We emphasize the precise modification of Pontryagin's maximum princ…
Size-Selective Threshold Harvesting under Nonlocal Crowding and Exogenous Recruitment
Jiguang Yu, Louis Shuo Wang, Ye Liang
We propose a nonlinear size-structured fishery model for externally recruited stocks under size-selective harvesting. The population density satisfies a McKendrick--von Foerster tr…
Age-Structured Harvesting Models: A Structural Comparison of Rate-Control and Effort-Control Optimality Systems
Jiguang Yu, Louis Shuo Wang, Ye Liang
We study optimal harvesting in continuous-time, age-structured population models of McKendrick--von Foerster type, and we compare two harvesting mechanisms. In the \emph{rate-contr…