Physics Business Biology Engineering Objectives to Optimize Efficiency Safety Accuracy Introduction Constraints Cost Weight Structural Integrity Challenges HighDimensional Search Spaces ID: 801563
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Slide1
Introduction
Slide2Applications of Optimization
PhysicsBusinessBiologyEngineeringObjectives to OptimizeEfficiencySafetyAccuracy
Introduction
ConstraintsCostWeightStructural IntegrityChallengesHigh-Dimensional Search SpacesMultiple Competing ObjectivesModel Uncertainty
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Slide3Queen Dido’s Optimization Problem
A History3
Slide4Calculus
Numerical AlgorithmsArtificial IntelligenceA History4
Slide5Optimization Process
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Slide6Design Point
Design VariablesObjective FunctionFeasible SetMinimizerBasic Optimization Problem
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Slide7Basic Optimization Problem
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Slide8Constraints
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Slide9Constraints
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Slide10Univariate Function
Critical Points10
Slide11Univariate
Function the first-order necessary condition (FONC)
the second-order necessary condition (SONC)
Conditions for Local Minima11
Slide12Conditions for Local Minima
Multivariate Functions the first-order necessary condition (FONC)
the second-order necessary condition (SONC)
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Slide13Contour Plots
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Slide14Overview
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Slide15Summary
Optimization in engineering is the process of finding the best system design subject to a set of constraintsOptimization is concerned with finding global minima of a functionMinima occur where the gradient is zero, but zero-gradient does not imply optimality15