CSE543T: Algorithms for Nonlinear Optimization Yixin Chen Department of Computer Science

1
CSE543T Algorithms for Nonlinear
OptimizationYixin ChenDepartment of Computer
Science EngineeringWashington University in St
Louis

• Fall, 2008

2
Nonlinear Programming (NLP) problem

• Minimize f(x)
• (optional) Subject to h(x) 0
• g(x) lt 0
• Characteristics
• variable space X continuous, discrete, mixed,
  curves
• Decision variables, control variables, system
  inputs
• function properties
• Closed form, evaluation process, stochastic,

3
Sensor network optimization

• Variables
• Number of sensors
• Locations of sensors
• Functions
• Minimize the maximum false alarming rate
• Subject to minimum detection probability gt 95
• Highly nonlinear functions
• Based on a Gaussian model and voting procedure
• Computed by a Monte-Carlo simulation

4
Sodoku
5
Why study nonlinear optimization?

• Optimization is everywhere
• Constraints are everywhere
• The world is nonlinear (curvature and local
  optima)
• Plenty of applications
• Investment, networking design, machine learning
  (NN, HMM, CRF), data mining, sensors, structural
  design, bioinformatics, medical treatment
  planning, games
• Nonlinear optimization is difficult
• Curse of dimensionality, among many other reasons

6
Goals of the course

• Introduce the theory and algorithms for nonlinear
  optimization
• One step further to the back of the blackbox
• Able to hack solvers
• But not too much gory details of mathematics
• Hands-on experiences with optimization packages
• Know how to choose solvers
• Understanding of the characteristics of
  problems/solvers
• Mathematical modeling
• Modeling languages
• CSE applications
• Help solve problems in your own research

7
Overview of the course

• Unconstrained optimization (6 lectures)
• Convex constrained optimization (3 lectures)
• General constrained optimization (12-14 lectures)
• Penalty methods
• Lagrange methods
• Dual methods

8
Assignments and grading

• Three or four homework (40)
• One project (30)
• In-class presentations
• Reports
• One final exam (30)