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# Note for Optimization in Engineering - OE by Harjot Singh

• Optimization in Engineering - OE
• Note
• Thapar University -
• Computer Science Engineering
• B.Tech
• 14 Topics
• 7996 Views
0 User(s)

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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

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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

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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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Some Optimization Problems Find the shortest path between the two points A and B in a horizontal plane Shirish Shevade Numerical Optimization