Cour Number: IE240
Cour Title: Optimization Methods in Industrial Engineering
Number of Units: 4
Schedule: Three hours of lecture and one hour of discussion per week.
Prerequisites: IE 230 Operations Rearch I (Linear Programming)
Catalog Description
Nonlinear optimization models and their properties. Characterizations of models (constrained vs unconstrained, convex, parable, quadratic; etc). First and Second Order Optimality Conditions and their u in algorithmic development. Solution algorithms for lected models.
Expanded Description
1. Solution of linear equations; approximation by truncated Taylor ries; convexity of ts;
convexity of functions; quadratic forms; positive definite and midefinite matrices;
Newton-Raphson method for solving nonlinear equations; cant method for solving nonlinear equations;
2. Unconstrained optimization; local & global optima; first and cond order conditions for
大名单local optima; Newton-Raphson method for finding a stationary point; steepest descent method; conjugate directions; quasi-Newton arch methods; one-dimensional
minimization (line-arch methods)
3. Separable (piecewi-linear) programming; grid refinement algorithm
4. Constrained nonlinear optimization; Lagrangian function; Lagrange multiplier method;
Karush-Kuhn-Tucker optimality conditions; constraint qualifications; Lagrangian duality 5. Feasible direction arch methods for constrained optimization; quential LP algorithm;
generalized reduced gradient algorithm
6. Quadratic programming (QP); Lagrangian dual of QP problem; complementary pivoting
algorithm for QP; QP model for portfolio optimization; quential QP algorithm for
nonlinear programming
7. Penalty and barrier functions for constrained optimization; u of barrier function in path-
following interior point methods for LP.
8. Other optimization methods and applications may be introduced at the discretion of the
instructor, e.g.,
• Fractional programming,
• Non-convex parable programming,
• Optimization in Pattern Recognition,
• Financial Optimization models,
• Posynomial & Signomial Geometric Programming,
合家欢乐7
• Pooling Problems,
对爱的理解• Applied Statistics (e.g., maximum likelihood estimation, regression)
Cour Objectives and Role in Program:
This cour is an elective cour in the IESM program. It builds upon knowledge that students have acquired in the core cours IE230 and IE231 (Operations Rearch I and II) This cour aims to provide the necessary background so students can pursue applications and further development of optimization models in other cours and in their thesis. Students are expected to develop reasonable modeling skills allowing them to cast appropriate real
world problems as optimization problems and to solve them with available software. They are expected to understand the limitations as well as the advantages of the algorithms, and be able to interpret their output. Small examples are ud to illustrate the connections of this cour with other areas (e.g., Simulation: fitting of data to distribution functions; Economics: Duopolies; Statistics: least squares approximation; Inventory & Production management: economic order quantity, etc).
Learning Outcomes
By the end of the cour,
刑事警察
1. the student will understand the concepts of convexity of a t and convexity of a function;
the student will be able to recognize a quadratic form and to test it for convexity by
checking its Hessian matrix for positive midefiniteness; the student will be able to u the truncated Taylor ries to form linear and quadratic approximations of functions.
2. the student will be able to form a geometric interpretation of the Karush-Kuhn-Tucker
optimality conditions; the student should recognize characteristics of a problem which make the K-K-T conditions insufficient for (global) optimality, so that he or she will not regard a solution found by a arch algorithm as necessarily the best which can be
achieved.
3. the student will be able to approximate a parable nonlinear optimization problem, with
or without constraints, with piecewi-linear functions and to u an LP solver to find an approximate solution.
4. The student will understand the strategy of solving a nonlinear optimization problem by
solving a quence of more easily-solved approximations, e.g., quential LP, quential QP (quadratic programming), quential unconstrained minimization technique (SUMT), quential posynomial GP (approximating a signomial GP problem), quential monomial GP (approximating a posynomial GP problem).
Method of Evaluation:
Student learning will be evaluated on the basis of
• Completeness and quality of weekly homework assignments
• Grade on veral weekly quizzes
• Grade on midterm examination
• Grade on final examination
毛遂自荐造句• Participation in a Term Project and submission of a final report
索尼nx100
• Class participation
Required Textbook
海誓山盟
Operations Rearch: Applications and Algorithms,third edition, (Chapter12) by Winston, Wayne L. Duxbury Press, (an imprint of Wadsworth Publishing Company), Belmont, CA. Recommended References
The textbook is supplemented with written materials, including applications, provided by the instructor, and the following on-line material:
• Convex Optimization, by Stephen Boyd and Lieven Vandenberghe, Cambridge University Press, 2004 (available on-line at a coauthor’s web site:
www.stanford.edu/~boyd/rearch.html)
• Applied Optimization: Formulation and Algorithms for Engineering Systems, by Ross Baldick, Department of Electrical and Computer Engineering, The University of
Texas at Austin (available on-line from the author’s web site at
Software:
• LINGO (LINDO Systems, Inc.)
• MATLAB Optimization Toolbox
如何学习好
Modified by: Dennis Bricker
Revision approved: May 29, 2006
