MATH 707 Nonlinear Optimization
course in real analysis in finite dimensional spaces.
Optimization has applications in many fields, both in research and industry, and forms an integral part of parameter estimation and control, as well as machine learning. This course aims to give doctoral students an overview of the current state of the art in nonlinear optimization. We will discuss the theoretical underpinnings and convergence of various optimization approaches and offer practical guidelines for their use and implementation. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming, and semi-definite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and sub-gradient optimization, interior-point methods and penalty and barrier methods.
Offered
Spring