In The Name of GOD


Sharif University of Technology

Department of Aerospace Engineering




Advanced Optimization





Hassan Haddadpour (



Finding the best design with the available resources is the goal of design optimization. Many of the design problems in aerospace systems (and also other areas) can be cast as optimization problems. These problems can then be solved using the optimization techniques. In this sense, optimization is only a mathematical tool. One can model the problems well only with a good understanding of the theory behind optimization. This course introduces you to the optimization theory and tells you how it can be applied to solve design problems. In this course we will deal with continuous optimization methods with emphasis upon nonlinear programming. At the end of the course the student should master most of the issues in numerical optimization.




1)     Basic Concepts


                  Optimization Concepts

                  General Problem Statement

                  Classification of Optimization Problems

                  Optimization Techniques

2)     Linear Programming


                  Standard Linear Programming Form

                  Possible Solutions

                  The Simplex Method

                  Revised Simplex Method

                  Duality in Linear Programming

                  Sensitivity Analysis

3)     One Variable Optimization


                  Search Methods

                  Polynomial Approximations

                  Golden Section Method

                  Other Methods

                  Comparison of the Methods

4)     Unconstrained Optimization Techniques


                  Zero-Order Methods

                  First-Order Methods

                  Second-Order Methods

                  Convergence Criteria

5)     Constrained Optimization Techniques

Direct Methods


                  Random Search

                  Sequential Linear Programming

                  The Method of Feasible Directions

                  Generalized Reduced Gradient Method

                  Sequential Quadratic Programming

Indirect Methods


                  The Exterior Penalty Function Method

                  The Interior Penalty Function Method

                  The Extended Interior Penalty Function Method

                  The Augmented Lagrange Multiplier Method

6)     Further Topics in Optimization

                  Structural Optimization

                  Mutiobjective Optimization

                  Genetic Algorithms



The final grade will be calculated as follows:

        Homeworks (30%)

        Design project (20%)

        Mid-Term Exam (20%)

        Final Exam (30%)



Students who successfully complete the course will demonstrate the following outcomes:

        Become familiar with optimization methods

        Mathematical modeling of optimization problems

        Implementation of the algorithms discussed and solve realistic design problems


Related Web Sites (Vanderplaats R&D) (search engine at this site to look for software on optimization) (Tom Cavalier's Optimization Links) (Network Enabled Optimization System Guide)



       1.         G. N. Vanderplaats, Numerical Optimization Techniques for Engineering Design: With Applications, McGraw-Hill, 1984.


Other References

       2.         Haftka, R. T. and Gurdal, Z., Elements of Structural Optimization, third edition, Kluwer Academic Publishers, 1992.

       3.         R. Fletcher, Practical Methods of Optimization, Second Edition, Wiley, 1987.

       4.         SS Rao, Engineering Optimization: Theory and Practice, 3rd Ed, Wiley, 1996.