MSIS 22:711:652, Spring 2003 Class meets on Wednesdays 1-3:50pm

Instructor: Farid Alizadeh

telephone: 973-353-5488(Newark) 732-445-4857 (New Brunswick)

e-mail: alizadeh@andromeda.rutgers.edu

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Syllabus

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Notes

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Last changed: 04/21/2003, 11:55:21

There are no exams or home works or exams for this course

For each lecture a student volunteer should take charge, take notes from the lectures, prepare a LaTeX document from them and e-mail them to me, so I post them in the web page. See the Notes page for details

Each student should also give a presentation, either of a research paper or a project he or she is undertaking.

There are no textbooks assigned for this course. Appropriate texts and papers will be available in the reserves section of the library.

Topics: A. Unconstrained Optimization

Convex functions (read Bertsekas

Optimality conditions for optimization over convex and related functions

The steepest descent method

Line search along a given direction

Newton's Method

Quasi-Newton Methods

Truncated Newton Methods

Topics: B. Constrained Optimization (nonlinear Programming)

Cone LP and extension of linear programming to convex programming

Properties of convex sets: Separation theorems, Farkas Lemma, Caratheodory's Theorem, Helly's Theorem

Duality theory and complementarity problems

Linear Programming (LP), Quadratic Programming (QP), Quadratic Cone Programming (QCP), Semidefinite Programming (SDP)

Lagrangean duality and Karush Kuhn Tucker (KKT) conditions

Interior Point methods, and Logarithmic barrier functions

Application of interior point methods for LP, QP, QCP and SDP

Penalty Methods

Dual and Lagrangean methods

Other methods (SQLP, gradient projection, reduced gradient)

References:

Bertsikas, D. "Nonlinear Programming", Athena Scientific, 1995

Fiacco, A. and McCormick, G. "Nonlinear Programming, Sequential Unconstrained Minimization Techniques", SIAM Classics in applied Mathematics, Society for Industrial and Applied Mathematics, 1990

Luenberger, D. "Linear and Nonlinear Programming", Second Edition, Addison-Wesley, 1984

Mangasarian, O. "Nonlinear Programming", SIAM Classics in applied Mathematics, Society for Industrial and Applied Mathematics, 1994

MSIS 22:711:652, Spring 2003 Class meets on Wednesdays 1-3:50pm Instructor: Farid Alizadeh telephone: 973-353-5488(Newark) 732-445-4857 (New Brunswick) e-mail: alizadeh@andromeda.rutgers.edu
Home Syllabus Resources Notes Papers	Last changed: 04/21/2003, 11:55:21 There are no exams or home works or exams for this course For each lecture a student volunteer should take charge, take notes from the lectures, prepare a LaTeX document from them and e-mail them to me, so I post them in the web page. See the Notes page for details Each student should also give a presentation, either of a research paper or a project he or she is undertaking. There are no textbooks assigned for this course. Appropriate texts and papers will be available in the reserves section of the library. Topics: A. Unconstrained Optimization Convex functions (read Bertsekas Optimality conditions for optimization over convex and related functions The steepest descent method Line search along a given direction Newton's Method Quasi-Newton Methods Truncated Newton Methods Topics: B. Constrained Optimization (nonlinear Programming) Cone LP and extension of linear programming to convex programming Properties of convex sets: Separation theorems, Farkas Lemma, Caratheodory's Theorem, Helly's Theorem Duality theory and complementarity problems Linear Programming (LP), Quadratic Programming (QP), Quadratic Cone Programming (QCP), Semidefinite Programming (SDP) Lagrangean duality and Karush Kuhn Tucker (KKT) conditions Interior Point methods, and Logarithmic barrier functions Application of interior point methods for LP, QP, QCP and SDP Penalty Methods Dual and Lagrangean methods Other methods (SQLP, gradient projection, reduced gradient) References: Bertsikas, D. "Nonlinear Programming", Athena Scientific, 1995 Fiacco, A. and McCormick, G. "Nonlinear Programming, Sequential Unconstrained Minimization Techniques", SIAM Classics in applied Mathematics, Society for Industrial and Applied Mathematics, 1990 Luenberger, D. "Linear and Nonlinear Programming", Second Edition, Addison-Wesley, 1984 Mangasarian, O. "Nonlinear Programming", SIAM Classics in applied Mathematics, Society for Industrial and Applied Mathematics, 1994