Note: Some of the material referenced below may be copyrighted, and hence is not generally available by clicking on it. Please email me, rbk@louisiana.edu, and I will email you either a Postscript or a PDF copy of the appropriate excerpts, according to the ``fair use" provision of the copyright law.
Home
page for the course
Bibliography
for the course in PDF format
Recommended references for the first part of the course:
The first two chapters of Convexification and Global Optimization in
Continuous and MixedInteger Nonlinear Programming: Theory, Algorithms,
Software, and Applications, Mohit Tawarmalani and Nikolaos Sahinidis,
Kluwer Academic Publishers, 2002 will be used, as well as C. A. Floudas,
Detyerministic
Global Optimization: Theory, Methods, and Applications, Kluwer Academic
Publishers, 2000.
Topic no.  Description  Explanation / References / Projects 
1.  Overview of the course and a review of global optimization principles


2.  A review of validated computation principles 

3.  A problem: Interaction of constraints, objective, and global estimates. 

4.  Comparison of various linear underestimators, interval evaluations, and Taylor models  The introductory sections of the Tawarmalani and the Floudas books, as well as class notes. Several techniques are exhaustively applied to an illustrative example. 
5.  Solving the resulting quadratic programming problem  See the web book, Linear Complementarity, Linear and Nonlinear Programming: Internet Edition 
6  Validating the solution of the linear programming problem 

7.  An overestimation / underestimation arithmetic  
8.  A study of duality in linear programming  
9.  Refinement of relaxations with the "sandwich" algorithm, etc.  
10.  Possible LP solvers for the relaxed problem 

11.  Languages for modeling 
Problems of interest are commonly expressed in these languages. 
12.  Experimentation over the web 

13.  The alphaBB approach 

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