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

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

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

Math 364

Here is Chapter 16.

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

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.

Here is a compilation of the quizzes.

(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) [Tu Oct 29] Chapter 11, Exercise 8

(20) [Th Oct 31] Chapter 11, Modeling Problem 4

(21) [Tu Nov 05] Chapter 11, Modeling Problem 13

(22) [Th Nov 07] Chapter 11, Modeling Problem 18

(23) [Tu Nov 12] Chapter 11, Exercise 17

(24) [Th Nov 14] Chapter 12, Exercise 3

(25) [Tu Nov 19] Chapter 13, Exercise 7(a,b)

(26) [Th Nov 21] Chapter 13, Exercise 7(c,d)

(27) [Tu Dec 03] Chapter 13, Exercise 7e

(28) [Th Dec 05] Chapter 16, Exercise 1b

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.

Check out the solutions.

Time: 10:10AM -- 12:10PM

Place: We will use our normal classroom.

I am providing a few practice exams. Please note that the content will have significant overlap with the topics we studied in class. However, they may also include topics which we did not consider. Practice Exams: Exam1, Exam2, Exam3.

Here are selected solutions to the practice exams. Beware! My solutions have not been carefully checked and there are problems with the questions on Exam2 -- but the flavor of the questions is still good.

The exam will have one question asking you to compose an executive summary. The problem of interest is Modeling Problem 19 (page 146 of the text). The solution will be provided on the exam, but you may wish to solve the problem and think about the solution before the exam.

Math 564

A proof that Compass Search convergest to a stationary point.

Notes on Optimization Over a Simplex.

Notes on Feasible Direction Methods.

Papers on Total Variation Denoising: RyOsFa1992.pdf, Ch2004.pdf, ChGoMu1999.pdf, GoYi2005.pdf.

unconstrained local minimum (maximum)

unconstrainted global minimum (maximum)

stationary point

singular, nonsingular

locally stable

coercive

isolated stationary point

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.

Section 3.3, Exercise 3.

Section 4.2, Exercises 1,2. Data for part (b) of Exercise 2

Time: 9:10AM - 10:00AM

Place: CUE 409

Here is the takehome question.

Time: 9:10AM - 10:00AM

Place: CUE 409

Time: 9:10AM - 10:00AM

Place: CUE 409

Time: 8:00AM - 10:00AM

Place: CUE 409

Coming Soon!

- 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]

I like to write short human interest pieces.

I like to ask questions.

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