Mest 16888 ESD.J7 Multidisciplinary System Design Optimization(MSDO) Numerical Optimization Lecture 6 23 February 2004 Karen willcox C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
1 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Multidisciplinary System Multidisciplinary System Design Optimization (MSDO) Design Optimization (MSDO) Numerical Optimization I Lecture 6 23 February 2004 Karen Willcox
Mest Today's Topics 16888 E77 Existence Uniqueness of an optimum Solution Kuhn-Tucker Conditions Convex Spaces Unconstrained problems Linear Programming C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
2 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Today’s Topics Today’s Topics • Existence & Uniqueness of an Optimum Solution • Kuhn-Tucker Conditions • Convex Spaces • Unconstrained Problems • Linear Programming
Mest Disclaimer 16888 ESD.J7 This is not a classic optimization class The aim is not to teach you the details of optimization algorithms, but rather to expose you to different methods We will utilize optimization techniques-the goal is to understand enough to be able to utilize them wisely If you plan to use optimization extensively in your research, you should take an optimization class, e.g 15093 C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
3 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Disclaimer! Disclaimer! • This is not a classic optimization class ... • The aim is not to teach you the details of optimization algorithms, but rather to expose you to different methods. • We will utilize optimization techniques – the goal is to understand enough to be able to utilize them wisely. • If you plan to use optimization extensively in your research, you should take an optimization class, e.g. 15.093
Mest Learning objectives 16888 ES077 After the next two lectures you should be familiar with what gradient-based optimization techniques are available understand the basics of how each technique works be able to choose which optimization technique is appropriate for your problem understand what to look for when the algorithm terminates understand why the algorithm might fail C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
4 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics Learning Objectives Learning Objectives After the next two lectures, you should: • be familiar with what gradient-based optimization techniques are available • understand the basics of how each technique works • be able to choose which optimization technique is appropriate for your problem • understand what to look for when the algorithm terminates • understand why the algorithm might fail
Mlesd How to Choose an Algorithm? 850. Number of design variables Type of design variables(real/integer, continuous/discrete) Linear/nonlinear Equality/inequality constraints Discontinuous feasible spaces Initial solution feasible /infeasible Simulation code runtime C Massachusetts Institute of Technology - Prof de Weck and Prof Willcox Engineering Systems Division and Dept of Aeronautics and Astronautics
5 © Massachusetts Institute of Technology - Prof. de Weck and Prof. Willcox Engineering Systems Division and Dept. of Aeronautics and Astronautics How to Choose an Algorithm? How to Choose an Algorithm? • Number of design variables • Type of design variables (real/integer, continuous/discrete) • Linear/nonlinear • Equality/inequality constraints • Discontinuous feasible spaces • Initial solution feasible/infeasible • Simulation code runtime