5 papers · 1 filter
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
In this paper, we formulate and analyze an original infinite-horizon bioeconomic optimal control problem for a nonlinear, size-structured fish population. Departing from standard e…