DAMTP 2008/NA06
On the convergence of a wide range of trust region
methods for unconstrained optimization1
M.J.D. Powell
Abstract: We consider trust region methods for seeking the unconstrained minimu
Lecture 14: Accelerated PG Method, Incremental PG
Method, Stochastic Optimization
Nesterovs accelerated rst order method
Iteration complexity estimate
First order method for composite nonsmooth con
Lecture 12: Analysis of AGP Method and Extensions
Error bounds for optimization problems
Linear convergence analysis of AGP method
Extension to nonconvex quadrattic QP
Extension to nonsmooth optim
Lecture 11: Approximate Gradient Projection
Linear convergence without strong convexity: composite
objective function f (x) = g (Ex) + b x.
A general framework for approximate gradient projection
M
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 10
Zhi-Quan Luo
Lecture 10: Issues
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 9: Penalty Methods and Multiplier M
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 8: Constrained Optimization: Dualit
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 7: Constrained Optimization: Lagran
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 6: Optimization over a Convex Set
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 5: Second Order Methods
Newtons Me
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 4: Optimal First Order Methods
Unc
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 3: Additional First Order Methods
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 2
Zhi-Quan Luo
Lecture 2: Gradient
EE5239 Introduction to Nonlinear Optimization
Zhi-Quan (Tom) Luo
Department of Electrical and Computer Engineering
University of Minnesota
[email protected]
Lecture 1
Zhi-Quan Luo
Lecture 1 Unconstrai
November 23, 1991
ERROR BOUNDS AND CONVERGENCE ANALYSIS
OF FEASIBLE DESCENT METHODS: A GENERAL APPROACH
by
Zhi-Quan Luo and Paul Tseng
ABSTRACT
We survey and extend a general approach to analyzing the
Course Notes on First Order Optimization Methods
Zhi-Quan Luo, University of Minnesota
Spring, 2011
1
Introduction
So far we have studied various rst order methods for unconstrained smooth convex opti
Course Notes on First Order Optimization Methods
Zhi-Quan Luo, University of Minnesota
Spring, 2011
Consider a convex dierentiable minimization problem:
minimize f (x)
subject to x X
(1)
where X IRn i