Vector spaces and matrices, transformations, eigenvalues and eigenvectors, norms; geometrical concepts ‐‐ hyperplanes, convex sets, polytopes and polyhedra; unconstrained optimization ‐ condition for local minima; one dimensional search methods ‐‐ golden section, fibonacci, newtons, secant search methods; gradient methods ‐‐ steepest descent; newton's method, conjugate direction methods, conjugate gradient method; constrained optimization ‐‐ equality conditions, lagrange condition, second order conditions; inequality constraints ‐‐ karush‐kuhntucker condition; convex optimization; introduction to assignment problem, decision analysis dynamic programming and linear programming

1. An Introduction to Optimization, Edwin K. P. Chong and Stanislaw H. zak, Wiley Interscience, 2008.

2. D. G. Luenberger, Optimization by vector space methods, New York, Wiley, 1969.

3. Convex Optimization Theory, D. P. Bertsekas, Athena Scientific optimization and computation series, 2009

4. Introduction to Operations Research, rederick S. Hillier, Gerald J. Lieberman, McGraw‐Hill, 2010

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