Tom Asaki's Website

My Contact Info

Find Me:

Office: Neill 228
email: tasaki@wsu.edu

Office Hours:

MonWed 11:00 - 12:00
TueThu 9:00 - 10:00
and by appointment

Address:

Department of Mathematics
103 Neill Hall
P.O. Box 643113
Washington State University
Pullman, WA 99164-3113

A Bit About Me

I managed to finish my doctorate in physics in 1995 right here at WSU (Go Cougs!). I spent the next 13 years as a postdoc and staff member at Los Alamos National Laboratory. In 2008, I returned to WSU as an Associate Professor, but this time in the Mathematics Department!

Before all of that, I spent time hitchhiking around the country, working odd jobs and becoming a classic video game champion. I have lived in California, Washington, Idaho, Montana, New Mexico, and occasionally nowhere in particular. My favorite places are the empty uninhabited areas of the Great Basin and Rocky Mountains (not Colorado!). My family lines stretch back to the cultures of Japan, England, Scotland, Norway, and Central Asia.
My Erdös number is 4. My Bacon number is 3.

Principles of Optimization
Math 364

Important Information

Here is the course Syllabus.

Resources

Here is the course textbook (updated August 15).

Here is the software you will need to complete much of the homework:

ExampleMatlab.m Example Code for Matlab
ExampleOctave.m Example Code for Octave
mip.m ShowSolution.m Fancy Code once you try out the above code

Homework Self-Study

Be able to complete all of the Exercises presented in the text. This should be the focus of your self-study. For problems to be turned in and graded, see the next section.

Here are a few examples of well-written homework problem solutions. Updated Friday September 27.

Here are some Quiz Solutions. Updated Sunday September 29.

In this paper, you can read how Dantzig describes the circumstanced behind the development and implementation of the Simplex Method.

Homework for Submission

(##) [Due Date] Assignment
(01) [Th Aug 22] Chapter 2, Exercise 1
(02) [Tu Aug 27] Chapter 2, Exercise 8
(03) [Th Aug 29] Chapter 3, Exercise 4
(04) [Tu Sep 03] Chapter 3, Exercises 5c and 8c
(05) [Th Sep 05] Chapter 4, Exercise 4
(06) [Tu Sep 10] Chapter 4, Exercises 6a and 6b
(07) [Th Sep 12] Chapter 5, Exercise 2
(08) [Tu Sep 17] Chapter 6, Exercise 2
(09) [Th Sep 19] Chapter 7, Exercise 1a
(10) [Tu Sep 24] Chapter 7, Exercise 2
(11) [Th Sep 26] Chapter 8, Exercise 7a and 7b
(12) [Tu Oct 01] Chapter 9, Exercise 5
(13) [Th Oct 03] Chapter 11, Exercise 1 (not modeling problem 1)
(14) [Tu Oct 08] Chapter 11, Exercise 2 (not modeling problem 2)
(15) [Th Oct 10] Chapter 11, Exercise 3 (not modeling problem 3)
(16) [Tu Oct 15] Chapter 11, Exercise 4
(17) [Th Oct 17] Chapter 11, Modeling Problem 9 (start early)
(18) [Tu Oct 22] Chapter 11, Modeling Problem 5
(19) [Th Oct 24] Chapter 11, Exercise 8

Midterm Exam

Date: Thursday, October 3
Time: during normal class time
Place: we will use our normal classroom
Please read the cover sheet of the exam before coming to the exam.

Final Exam

Date: Thursday, December 12
Time: 10:10AM -- 12:10PM
Place: TBD (likely our normal classroom)

Convex and Nonlinear Optimization
Math 564

Resources

Course Syllabus

A proof that Compass Search convergest to a stationary point.

Notes on Optimization Over a Simplex.

Notes on Feasible Direction Methods.

Definitions

As part of your homework, you will need to formally define various mathematical terms. What follows is a list of terms that you should include, though it may not be complete. This list will be regularly updated.

unconstrained local minimum (maximum)
unconstrainted global minimum (maximum)
stationary point
singular, nonsingular
locally stable
coercive
isolated stationary point

Homework Assignments

Your homework will be collected in a single document which you will keep at overleaf.com and you must provide me with edit priviledges (for feedback and grading). You may wish to start with this homework assignment template and example figure.

Section 1.1, Exercises 1,2,4,8.
Section 1.2, Exercises 1,3,7,12.
Section 1.3, Exercises 1,3.
Section 1.4, Exercises 1,8.
Section 1.6, Exercise: On page 145 of the text, Bertsekas states "These estimates suggest a more favorable convergence rate than the one of steepest descent." Justify this statement.
Section 1.7, Quasi-Newton Homework.
Section 1.8, Show that for a strictly convex function, the Nelder-Mead Simplex method never utilizes the shrink step.
Section 2.1, Exercises 8,11(part 3)
Section 2.2, Optimization over a Simplex Homework.
Section 2.3, Gradient Projection Homework.
Section 3.1, Equality Constrained Optimization Homework.

Midterm Exam #1

Date: Monday, September 16
Time: 9:10AM - 10:00AM
Place: CUE 409
Here is the takehome question.

Midterm Exam #2

Date: Monday, October 14
Time: 9:10AM - 10:00AM
Place: CUE 409

Midterm Exam #3

Date: Wednesday, November 13
Time: 9:10AM - 10:00AM
Place: CUE 409

Final Exam

Date: Friday, December 13
Time: 8:00AM - 10:00AM
Place: CUE 409

Research

Coming Soon!

Publications

T.J. Asaki and H.A. Moon, "Anisotropic Variation Formulas for Imaging Applications," AIMS Mathematics, vol. 4, (2019).
H.A. Moon and T.J. Asaki, "A Finite Hyperplane Traversal Algorithm for 1-Dimensional $L^1pTV$ Minimization, for $0 < p \leq 1$," Computational Optimization and Applications, vol. 61(3), (2015).
Nonasymptotic Densities for Shape Reconstruction
H.A. Van Dyke, K.R. Vixie and T.J. Asaki, "Cone Monotonicity: Structure Theorem, Properties, and Comparisons to Other Notions of Monotonicity," Abstract and Applied Analysis, vol. 2013, (2013).
B. Van Dyke and T.J. Asaki, "Using QR Decomposition to Obtain a New Instance of Mesh Adaptive Direct Search with Uniformly Distributed Polling Directions," J. Optim. Theory Appl., vol. 159, pp. 805-821, (2013).
M.A. Abramson, T.J. Asaki, J.E. Dennis Jr., R. Magallanez Jr. and M.J. Sottile, "An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions," Struct. Multidisc. Optim., vol. 45, pp. 53-64, (2012).
K.R. Vixie, K. Clawson, T.J. Asaki, G. Sandine, S.P. Morgan and B. Price, "Multiscale Flat Norm Signatures for Shapes and Images," Applied Mathematical Sciences, vol. 4, no. 14, pp. 667-680, (2010).
T.J. Asaki, "Quantitative Abel Tomography Robust to Noisy, Corrupted and Missing Data," Optim. Eng., vol. 11, pp. 381-393, (2010).
T.J. Asaki, K.R. Vixie, M. Sottile and P. Cherepanov, "Image Denoising by Regularization on Characteristic Graphs," Applied Mathematical Sciences, vol. 4, pp. 2541-2560, (2010).
T. Le, R. Chartrand and T.J. Asaki, "A Variational Approach to Reconstructing Images Corrupted by Poisson Noise," J. Math. Imaging Vis., vol. 27, pp. 257-263, (2007).
[more coming soon]

Extras

I like to write short human interest pieces.

I like to ask questions.

Cities Puzzler

Classic video game buff? Check out the entertaining documentary that includes me! Man vs Snake