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Intro
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Classroom Contents
New Trends in Nonlinear Optimization
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- 1 Intro
- 2 Outline
- 3 Methods for Nonlinear Optimization
- 4 Gradient Methods Steepest descent method (Cauchy 1847). Find the best point along the
- 5 Conjugate Gradient (CG) Methods
- 6 Quasi-Newton (QN) Methods
- 7 2.1 Nonmonotone Gradient Methods
- 8 Properties and Extensions of BB Method Convergence properties for quadratic optimization
- 9 Efficiency Evidences for Nonmonotone Gradient Method
- 10 2.2 Efficient Monotone Gradient Methods?
- 11 Dai-Yuan Monatone Gradient Method A variant of Yuan stepsize (D. & Yuan 2005)
- 12 2.3 Equip BB with 2D Quadratic Termination Property?
- 13 BBQ Stepsize Theorem (2D quadratic termination)
- 14 BBQ for Extreme Eigenvalues Problems
- 15 2.4 Discussion
- 16 3.1 Hestenes Powell Augmented Lagrangian
- 17 Fletcher's Exact Penalty Function
- 18 3.2 General Constrained Optimization
- 19 Interior Paint Technique Inequality Constrained Optimization
- 20 Interior Point Methods vs Simplex Methods
- 21 3.3 Smooth Barrier Augmented Lagrangian (SBAL)
- 22 Advantages of SBAL
- 23 Discussion: SBALM for MINLP
- 24 Algorithms for Infeasible Stationary Points
- 25 Compare Penalty Method and ALM for OLVC
- 26 Some Concluding Remarks
