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Mathematical Formulation Using an Example
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Numerical Optimization
Continuous Versus Discrete Optimization
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Constrained and Unconstrained Optimization
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Global and Local Optimization
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Stochastic and Deterministic Optimization
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Convexity
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Optimization Algorithms
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Concept of a Solution – Recognizing a Local Minimum
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Nonsmooth Problems
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Overview of Algorithms
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Two Strategies: Line Search and Trust Region
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Search Directions for Line Search Methods
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Models for Trust-region Methods
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What is Scaling
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Line Search – Convergence of Line Search Methods
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Rate of Convergence – Convergence Rate of Steepest Descent
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Newton’s Method
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Quasi-newton Methods
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Trust Region
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The Cauchy Point Algorithm
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Global Convergence – Reduction Obtained by the Cauchy Point
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