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Introduction to optimization algorithms

Introduction and review of fundamentals Unconstrained optimization Optimization subject to equality constraints Nonlinear programming Linear programming Selected topics from dynamic programming, large-scale programming, and multicriteria optimization. Detailed Description and Outline. Topics: Introduction and review of fundamentals Unconstrained optimization Optimization subject to equality constraints Nonlinear programming Linear programming Selected topics from dynamic programming, large-scale programming, and multicriteria optimization Same as CSE Topical Prerequisites.

Differential calculus Linear algebra Computer programming Ability to reason in abstract terms. Engineering Science: 1. Instructional Objectives. By the end of the semester, the students should be able to do the following: 1. Formulate finite-dimensional optimization problems 1 2. Apply some sufficiency conditions to an optimization method to test whether a minimum or a maximum exists, and whether they are unique 1 3. Tell the difference between a local optimum and a global optimum 1 4.

Use the first- and second-order conditions for unconstrained optima to calculate minima and maxima 1 5. Use various computational algorithms for unconstrained optimization, including steepest descent, Newton's method, conjugate-direction methods, and direct search methods 1 6.

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Analyze convergence of the algorithms in 5 above 1 7. Use software for numerical computation of minima and maxima 1 , 6 8. Obtain analytic solutions to some optimization problems with equality constraints, using Lagrange multipliers 1 9. Obtain analytic solutions to some optimization problems with inequality constraints, again using Lagrange multipliers 1 Use various computational algorithms for constrained optimization, including penalty function methods, primal and dual methods, penalty and barrier methods, and convex programming 1 Introduction and review of fundamentals Unconstrained optimization Optimization subject to equality constraints Nonlinear programming Linear programming Selected topics from dynamic programming, large-scale programming, and multicriteria optimization.

An Introduction to Optimization | Wiley Online Books

Detailed Description and Outline. Topics: Introduction and review of fundamentals Unconstrained optimization Optimization subject to equality constraints Nonlinear programming Linear programming Selected topics from dynamic programming, large-scale programming, and multicriteria optimization Same as CSE Topical Prerequisites.


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Differential calculus Linear algebra Computer programming Ability to reason in abstract terms. Engineering Science: 1. Instructional Objectives.

2. Optimization Problems

By the end of the semester, the students should be able to do the following: 1. Formulate finite-dimensional optimization problems 1 2. Apply some sufficiency conditions to an optimization method to test whether a minimum or a maximum exists, and whether they are unique 1 3. Tell the difference between a local optimum and a global optimum 1 4. Use the first- and second-order conditions for unconstrained optima to calculate minima and maxima 1 5. Use various computational algorithms for unconstrained optimization, including steepest descent, Newton's method, conjugate-direction methods, and direct search methods 1 6.

Analyze convergence of the algorithms in 5 above 1 7. Use software for numerical computation of minima and maxima 1 , 6 8. Obtain analytic solutions to some optimization problems with equality constraints, using Lagrange multipliers 1 9. Obtain analytic solutions to some optimization problems with inequality constraints, again using Lagrange multipliers 1 Use various computational algorithms for constrained optimization, including penalty function methods, primal and dual methods, penalty and barrier methods, and convex programming 1 The process of determining the best design is called optimization.

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Thus we may wish to design the smallest heat exchanger that accomplishes the desired heat transfer, or we may wish to design the lowest-cost bridge for the site, or we may wish to maximize the load a robot can lift. Often engineering optimization is done implicitly. Using a combination of judgment, experience, modeling, opinions of others, etc.

Introduction to Optimization and Semidifferential Calculus

Some engineers are very good at this. The interactions are too complex and the variables too numerous to intuitively determine the optimum design. In this text we discuss a computer-based approach to design optimization. With this approach, we use the computer to search for the best design according to criteria that we specify.