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Optimization in Engineering

by Harjot SinghHarjot Singh
Type: NoteInstitute: Thapar University Course: B.Tech Specialization: Computer Science EngineeringOffline Downloads: 113Views: 5097Uploaded: 10 months ago

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Harjot Singh
Harjot Singh
Numerical Optimization Introduction Shirish Shevade Computer Science and Automation Indian Institute of Science Bangalore 560 012, India. NPTEL Course on Numerical Optimization Shirish Shevade Numerical Optimization
Introduction Optimization : The procedure or procedures used to make a system or design as effective or functional as possible (adapted from www.thefreedictionary.com) Why Optimization? Helps improve the quality of decision-making Applications in Engineering, Business, Economics, Science, Military Planning etc. Shirish Shevade Numerical Optimization
Mathematical Program Mathematical Program : A mathematical formulation of an optimization problem: Minimize f (x) subject to x ∈ S Essential Components of a Mathematical program: x: variables or parameters f : objective function S: feasible region What is a solution of this Mathematical Program? x ∗ ∈ S such that f (x ∗ ) ≤ f (x) ∀ x ∈ S x ∗ : solution, f (x ∗ ): optimal objective function value x ∗ may not be unique and may not even exist. Maximize f (x) ≡ − Minimize −f (x) Shirish Shevade Numerical Optimization
Mathematical Optimization The problem, Minimize f (x) subject to x ∈ S can be written as min x f (x) s.t. x ∈ S (1) Mathematical Optimization a.k.a. Mathematical programming Study of problem formulations (1), existence of a solution, algorithms to seek a solution and analysis of solutions. Shirish Shevade Numerical Optimization

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