UUM 526E - Optimization Techniques in Engineering

Course Objectives

1- To give a detailed understanding of numerical optimization concepts and mathematical conditions for optimality
2- To understand and apply linear, non-linear, gradient-based, gradient-free, constrained and non-constrained optimization algorithms
3- To teach how to formulate a design problem as an optimization problem in the most efficient and correct way.
4- To teach how to choose the most convenient optimization algorithm for an optimization problem.
5- To give an understanding of how the results obtained by optimization procedure can be used towards a product

Course Description

Optimum Design Concepts, Lagrange Formulation, Karush-Kuhn Tucker necessary conditions, Linear Programming, Simplex method, Nonlinear Problems, Numerical Methods for Unconstrained Optimum Design, 1-D minimization, Steepest descent method, Conjugate gradient method, Newton’s method, Quasi Newton Methods, DFP method, BFGS method, Numerical Methods for Constrained Optimum Design, Sequential linear programming, Quadratic programming, Constrained steepest descent method, Constrained Quasi-Newton methods, Multi-objective Problems, Genetic Algorithms and Evolutionary Strategies, Multi-disciplinary Optimization and Sensitivity Analysis, Topology Optimization