- Office: Neill 228
- email: tasaki@wsu.edu

- Tuesday 1:10-4:00
- Wednesday 12:00-12:50
- and by appointment

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

Math 364

Additional notes on Integer Programming Methods.

Additional notes on Interior Point Methods.

We will be exploring many modeling problems during February in class. Please read one or two problems ahead of what we have completed in class.

Please consider this example of how to write acceptable homework solutions. Here is a more detailed example.

Refresher on partial derivatives.

Another refresher on partial derivatives.

Addtional practice on finding extrema of functions.

How to find eigenvalues of a matrix.

How to find the determinant of a matrix.

George Dantzig wrote a nice article on the early days of the Simplex Method for solving linear programs.

Some problems ask you to compose summary documents such as this example Executive Summary. I believe that it is a very valuable skill to be able to concisely and accurately summarize your work.

(01) [Mon Jan 14] (by 4 PM) Section 2, Exercises 1,2,3,4.

(02) [Tue Jan 22] Section 3, Exercises 3,4,5c,5d,6,8c,8d AND Section 4, Exercises 1,2.

(03) [Tue Jan 29] Section 4, Exercises 4,6d,6f AND Section 5, Exercises 2,3,6,7.

(04) [Tue Feb 05] Section 6, Exercises 2,3 AND Section 7, Exercises 1,2. For some of these exercises, you will need access to Matlab or Octave software. There are many options: (1) personal copy, (2) Math department software, (3) octave-online.net .

(05) [Tue Feb 12] Section 8, Exercises 3-8 AND Section 9, Exercises 1,5.

(06) [Tue Feb 19] Section 11, Exercises 2-5 AND Modeling Problems 4,8.

(07) [Tue Feb 26] Section 11, Exercises 6,8 AND Modeling Problems 5,7.

(08) [Tue Mar 05] Section 11, Exercises 9,10,11 AND Modeling Problem 20.

(09) [Tue Mar 19] Section 11, Exercise 12 AND Modeling Problem 10.

(10) [Tue Mar 26] Section 11, Exercises 15,17 AND Modeling Problems 16,19.

(11) [Tue Apr 02] Section 12, Exercises 1,2,3 AND Section 13, 3,6,7a.

(12) [Tue Apr 09] Section 13, Exercises 7b,c,d,e,f and 10,11.

(13) [Tue Apr 16] Consider the Puzzles and Games Inc. Problem of Section 11.17 and the formulation which does NOT enforce the "either-or" manufacturing constraint. Show that the optimal solution of the LP Relaxation is not integer-valued. Carefully solve the integer program using either the Branch and Bound method or the Cutting Plane method. You may use software to solve any LP Relaxation problems that arise in your solution process.

(14) [Tue Apr 23] Section 11, Modeling Problem 17. Model the problem as a binary integer program, then solve using the method of Implicit Enumeration.

Week 4.

Week 5.

Week 7.

Week 8.

Week 9.

Week 11.

Week 12.

Week 13.

Your quiz for week 15 is to complete the online course evaluation. This is a bonus quiz in that I will drop one extra low quiz score for everyone who completes this task.

Time: 9:10-10:25 (normal class time)

Location: Our normal classroom

Here is the exam cover sheet and the writing assignment problem.

You may wish to look over this example midterm from last semester. Our midterm will cover similar material, but may not be of this particular format. The level of skills and knowledge demonstration are representative of what I will expect of you.

Time: 10:10-12:10

Location: Our normal classroom

The exam will test your content knowledge and application skills in the areas of optimization which we considered throughout the course. The exam will consist of seven parts (questions) on the topics listed below. Please read this exam cover sheet to help you prepare.

- Constrained and unconstrained optimization of smooth functions using calculus methods.
- Standard forms of linear programs.
- Modeling mixed-integer programs whose solutions answer optimization questions from finance, mathematics, business or planning.
- Composing executive summaries or business memos which summarize optimization findings for the intended audience. The exam will concern the solution to Modeling problem 20 from Section 11.
- Concepts and practice of the Simplex Method.
- Concepts and practice of solving integer programs.
- Concepts and practice of interior point methods in optimization.

Math 490

The course syllabus contains most of the key information for the course including a detailed description, expectations, student evaluation criteria, and other topics. We are also providing a document on successful collaboration which you should definitely read.

This course is jointly run as Math 492 at Lewis-Clark State College and all of our activities will be run as a single course. The Math 492 professor is Dr. Heather Moon.

### Some Resources

Here is a link to Overleaf keyboard shortcuts and additional links to the Overleaf Manual and other Quick Guides such as one for LaTeX.

Here are two example problem descriptions. You can use these examples as guides when writing your own problem description.

### Major Deadlines to Keep in Mind

TBD -- MathFest Abstract Submission

March 14 -- Midterm Presentations

March 28 -- Midterm Report

April 25 -- Final In-Class Presentations

July 31 to August 3 -- MathFest

### Class Agenda Links

March 21

March 5

February 12

February 7

February 5

January 29

January 24

January 22

### Day 1 Information

Initial Tasks Documents:

### Templates for your Use

LaTeX report templates.

Time sheet template and accompanying class file.

This course is jointly run as Math 492 at Lewis-Clark State College and all of our activities will be run as a single course. The Math 492 professor is Dr. Heather Moon.

Here are two example problem descriptions. You can use these examples as guides when writing your own problem description.

March 14 -- Midterm Presentations

March 28 -- Midterm Report

April 25 -- Final In-Class Presentations

July 31 to August 3 -- MathFest

March 5

February 12

February 7

February 5

January 29

January 24

January 22

- YWCA -- Program/Donor Data Mining
- Hope Center -- Return on Investment
- NPCNF -- Stream Rating Curves
- NPCNF -- Hydrologic Event Detection
- NPCNF -- In-Class Presentation

Time sheet template and accompanying class file.

Coming Soon!

- 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]

I like to write short human interest pieces.

I like to ask questions.

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