Abstract: 
A quasi-differentiable function is one whose directional derivative at any reference point, viewed as a function of the direction, can be expressed as the difference of two positively homogeneous convex functions. Introduced by Pshenichnyi in 1969, this class was studied extensively for some time but has received limited attention in modern optimization, despite arising in many contemporary applications. To connect it more closely with the increasingly important difference-of-convex framework, we use the term quasi-difference-convex (quasi-dc) for quasi-differentiable functions that are also locally Lipschitz. Our work develops a unified treatment of iterative convex-programming-based descent methods for a broad class of composite quasi-dc problems, and establishes subsequential convergence, sequential convergence, and convergence rates, thereby extending the classical focus on subsequential convergence in quasi-differentiable optimization.


Bio-Sketch: 

Jong-Shi Pang was elected to the U.S. National Academy of Engineering in 2021 and is currently the Epstein Family Chair, Distinguished Professor, and Professor of Industrial and Systems Engineering at the University of Southern California. Previously, he held senior faculty and leadership positions at the University of Illinois Urbana-Champaign, Rensselaer Polytechnic Institute, Johns Hopkins University, the University of Texas at Dallas, and Carnegie Mellon University, and also served as a Program Director in the Division of Mathematical Sciences at the U.S. National Science Foundation. He is an internationally recognized leader in operations research and optimization, having received the 2019 John von Neumann Theory Prize, the 2003 George B. Dantzig Prize, and fellowship honors from both INFORMS and SIAM. His research has made fundamental contributions to optimization, variational inequalities, equilibrium programming, game theory, and constrained dynamical systems. He has published more than 160 papers in leading journals, authored several influential monographs, and previously served as Editor-in-Chief of SIAM Journal on Optimization and Mathematical Programming, Series B.