Course: MAT 453 3.0 Optimization (Compulsory)
Course content:
Maximizing/ minimizing objective function, Constraints, Categories of optimization problems and several illustrations; Functions of one variable/ several variables, Critical points, Maximizers and minimizers, Optimization with Hessian matrix of a function (quadratic forms, definiteness, principal minors), Optimization with Coercive functions; Convex sets, Convex functions, Optimization results associated with convexity, Convexity and Arithmetic-Geometric Mean Inequality; Newton’s Method, The Method of Steepest Decent, Beyond Steepest Decent; Least Square Fit, Subspaces and Projections, Minimum Norm Solutions of Underdetermined Linear Systems; : Convex programming; Karush-Kuhn-Tucker Theorem and Constrained Geometric Programming, Dual Convex Programming; History of Optimization- Classical Problems, Euler- Lagrange equation, Solutions of Classical Problems using Euler- Lagrange Equation.
Recommended Readings:
- Peressini, A. L., Sullivan, F. E., & Uhl, J. J., Jr. (1988). The Mathematics of Nonlinear Programming (Undergraduate Texts in Mathematics). Springer.
- Hoffmann, L.D, Bradley, G.L., & Rosen, K.H. (2005). Applied Calculus: For Business, Economics, and the Social and Life Sciences, 8th Expanded Edition (8th ed.). McGraw Hill.
- Applied Calculus – L.D. Hoffmann, G.L. Bradley, K.H. Rosen
- Blischke, W. R., & Murthy, P. D. N. (2000). Reliability: Modeling, Prediction, and Optimization (1st ed.). Wiley.
- Bittinger, M. L., Ellenbogen, D. J., & Surgent, S. J. (2012). Calculus and Its Applications (10th Edition) (10th ed.). Pearson.