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ME 366L Weekly Overview - Week 08

ME 366L Weekly Overview - Week 08 - solutions can be...

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Week Eight – Formulation of general nonlinear programs, distinction between local and global solutions, characteristics of solutions, two-dimensional examples Fundamentals of nonlinear programming Context: Many engineering and business problems are defined by nonlinear relationships. We start by introducing the nonlinear programming problem and present several two-dimensional examples to illustrate the nature of the feasible region and the characteristics of solutions. An important distinction is made between local and global solutions. We close with a discussion of the Hessian matrix which is used to determine the convexity of a smooth function. Purpose: To provide you with an introduction to the concepts and structure associated with nonlinear programs (NLPs), and to emphasis the extent to which global
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Unformatted text preview: solutions can be obtained with current technology. A secondary objective is to begin describing the different functional forms that are encountered in NLPs. Objectives: At the end of this lesson, you will be able to: 1. Graph and solve a two-dimensional nonlinear program. 2. Identify the solution characteristics of simple NLPs. 3. Explain the difference between local and global optimality, and identify the circumstances under which local solutions are also global. 4. Identify convex and concave functions and explain their importance in nonlinear programming. 5. Determine the Hessian matrix of a twice continuously differentiable function. 6. Explain the relationship between the Hessian and the convexity of a function. 7. Explain the limitations of computational techniques designed to solve NLPs....
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