Simultaneous approaches for dynamic optimization problems are surveyed and a number of
emerging topics are explored. Also known as direct transcription, this approach has a …

Publisher Summary This chapter provides an overview of the latest state of the art of
methods for numerical computation of Nash equilibria—and refinements of Nash equilibria …

This book describes a tool for mathematical modeling: the Python Optimization Modeling
Objects (Pyomo) software. Pyomo supports the formulation and analysis of mathematical …

Machine learning develops rapidly, which has made many theoretical breakthroughs and is
widely applied in various fields. Optimization, as an important part of machine learning, has …

Generative adversarial networks (GANs) form a generative modeling approach known for
producing appealing samples, but they are notably difficult to train. One common way to …

This monograph is about a class of optimization algorithms called proximal algorithms. Much
like Newton's method is a standard tool for solving unconstrained smooth optimization …

Abstract Extragradient method (EG)(Korpelevich, 1976) is one of the most popular methods
for solving saddle point and variational inequalities problems (VIP). Despite its long history …

Recent works have shown that stochastic gradient descent (SGD) achieves the fast
convergence rates of full-batch gradient descent for over-parameterized models satisfying …

During the recent years the interest of optimization and machine learning communities in
high-probability convergence of stochastic optimization methods has been growing. One of …

Bilevel optimization is a vital field of active research. Depending on its formulation it is part of
nonsmooth or nondifferentiable optimization, conic programming, optimization with …