GPGN 599

Numerical optimization for applied geophysics

 

Course description :

  
 
The course deals with the numerical techniques for solving optimization problems arising from applied geophysics such as inverse problems. The focus is on performing optimization of continuously differentiable functions that depend upon continuous variables. Both linear and nonlinear problems will be discussed. The course will start with unconstrained problems, and conclude with constrained optimization using interior-point methods. Different solution strategies, their implementation, capabilities, and limitations will be discussed.

 

Course objectives

  
  For students to understand and practice:
 
  • Basic theory on linear and nonlinear optimization techniques,
 
  • Numerical methods for their solutions,
 
  • Conjugate gradient method as a basic linear solver, and
 
  • Primal logarithmic barrier method for inequality constraints.

 

Study topics:

  
 
  • Fundamentals of unconstrained optimization
 
  • Earth's gravitational field: its global variations and various components for describing the field
 
  • Line search methods
 
  • Trust-region methods
 
  • Conjugate gradient methods
 
  • Quasi-Newton methods
 
  • Nonlinear least-squares problem
 
  • Basics of constrained optimization
 
  • Primal log barrier method

 

Textbook:

  
 
  • Nocedal, J., and Wright., S., 1999, Numerical optimization, Springer

 

Credit Hours: 3

  
     

 

Instructor:
  Dr. Yaoguo Li
  ygli@mines.edu
 

Phone: 303-273-3510
  Office: Green Center, 280N
     
     

Department of Geophysics • Colorado School of Mines • Golden, Colorado 80401
Phone (303) 273-3510 • E-mail: cgem@mines.edu

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