PPT-Survey of unconstrained optimization gradient based algorithms

Unconstrained minimization Steepest descent vs conjugate gradients Newton and quasiNewton methods Matlab fminunc Unconstrained local minimization The necessity for one dimensional searches. Select algorithms based on their popularity.. Additional details and additional algorithms in Chapter 5 of . Haftka. and . Gurdal’s. Elements of Structural Optimization. Optimization with constraints. Gradient descent. Key Concepts. Gradient descent. Line search. Convergence rates depend on scaling. Variants: discrete analogues, coordinate descent. Random restarts. Gradient direction . is orthogonal to the level sets (contours) of f,. for Geometry Processing. Justin Solomon. Princeton University. David . Bommes. RWTH Aachen University. This Morning’s Focus. Optimization.. Synonym(-. ish. ):. . Variational. methods.. This Morning’s Focus. Collin . Bezrouk. 2-24-2015. Discussion Reference. Some of this material comes from . Spacecraft Trajectory Optimization. (Ch. 7) by Bruce Conway.. Optimization Problem Setup. Optimization problems require the following:. multilinear. gradient elution in HPLC with Microsoft Excel Macros. Aristotle University of Thessaloniki. A. . Department of Chemistry, Aristotle University of . Thessaloniki. B. Department of Chemical Engineering, Aristotle University of Thessaloniki. Clint Jeffery. University of Idaho. Outline. Preliminary thoughts. AIGPW Chapters. EvoGames. Papers. Conclusions. Preliminary Thoughts. ANN and related technologies are rare in commercial games. Behavior of ANN-based agents often perceived as bizarre or unrealistic. Grigory. . Yaroslavtsev. http://grigory.us. Lecture 8: . Gradient Descent. Slides at . http://grigory.us/big-data-class.html. Smooth Convex Optimization. Minimize . over . admits a minimizer . (. Applications. Lecture . 6: . Optimize Finite Sum. Zhu Han. University of Houston. Thanks Dr. . Mingyi. Hong slides. 1. Outline (Chapter 10). Problem Formulation. Algorithms. The SAG and SAGA algorithm [Le Roux 12][. (x) = 0. h. i. (x) <= 0. Objective function. Equality constraints. Inequality constraints. Terminology. Feasible set. Degrees of freedom. Active constraint. classifications. Unconstrained v. constrained. :. Application to Compressed Sensing and . Other Inverse . Problems. M´ario. A. T. . Figueiredo. Robert . D. . Nowak. Stephen . J. Wright. Background. Previous Algorithms. Interior-point method. . Gradient descent. Key Concepts. Gradient descent. Line search. Convergence rates depend on scaling. Variants: discrete analogues, coordinate descent. Random restarts. Gradient direction . is orthogonal to the level sets (contours) of f,. Unconstrained minimization. Steepest descent vs. conjugate gradients. Newton and quasi-Newton methods. Matlab. . fminunc. Unconstrained local minimization. The necessity for one dimensional searches. Applications. Lectures 12-13: . Regularization and Optimization. Zhu Han. University of Houston. Thanks . Xusheng. Du and Kevin Tsai For Slide Preparation. 1. Part 1 Regularization Outline. Parameter Norm Penalties. Classification of algorithms. The DIRECT algorithm. Divided rectangles. Exploration and Exploitation as bi-objective optimization. Application to High Speed Civil Transport. Global optimization issues.