Weeks | Topics |
1 |
One-dimensional nonlinear numerical optimization: Gradient-based methods: Newton-Raphson method, Bisection method.
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2 |
One-dimensional nonlinear numerical optimization: Nongradient-based methods: golden-Section method, importance of one-dimensional nonlinear numerical optimization
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3 |
Multi-dimensional nonlinear numerical optimization: Problem definition, general update rule, mathematical basics.
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4 |
Multi-dimensional nonlinear numerical optimization: Analytical conditions for optimality
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5 |
Multi-dimensional nonlinear numerical optimization: First-order methods: Steepest-Descent, Conjugate-Gradient
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6 |
Multi-dimensional nonlinear numerical optimization: Second-order methods: Newton’s method
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7 |
Multi-dimensional nonlinear numerical optimization: Second-order methods: Modified Newton’s method, Cholesky factorization.
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8 |
Multi-dimensional nonlinear numerical optimization: Quasi-Newton method: Davidon-Fletcher-Powell method, Broydon-Fletcher-Goldfarb-Shanno method
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9 |
MIDTERM EXAM
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10 |
Multi-dimensional nonlinear numerical optimization: Second-order approximate methods: Gauss-Newton method, Levenberg-Marquardt method
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11 |
Applications: Single-Input Single-Output (SISO) Regression problem: polynomial model, RBF model, exponential model
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12 |
Applications: Single-Input Single-Output (SISO) Regression problem: SISO Artificial Neural Network (ANN) model.
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13 |
Applications: Multiple-Input Single-Output (MISO) Regression problem: MISO Artificial Neural Network (ANN) model.
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14 |
Applications: Multiple-Input Single-Output (MISO) Regression problem: Modeling and prediction by MISO Artificial Neural Network (ANN) model.
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