Optimization Algorithms Course WS 20/21 TU Berlin

Description

Optimization is one of the most fundamental tools of modern sciences. Many phenomena -- be it in computer science, artificial intelligence, logistics, physics, finance, or even psychology and neuroscience -- are typically described in terms of optimality principles. It is often easier to describe or design an optimality principle or a cost function rather than the system itself. However, if systems are described in terms of optimality principles, the computational problem of optimization becomes central to all these sciences.

This lecture aims give an overview and introdution to various approaches to optimization together with practical experience in the exercises. The focus will be on continuous optimization problems and is structured in three parts:

• Part 1: Downhill algorithms for unconstrained optimization:
  • gradient descent, backtracking line search, Wolfe conditions, convergence properties
  • covariant gradients, Newton, quasi-Newton methods, (L)BFGS
• Part 2: Algorithms for constrained optimization:
  • KKT conditions, Lagrangian
  • Log-barrier, Augmented Lagrangian, primal-dual Newton
  • SQP
• Part 3: Structured Problems, Libraries, Applications, Non-Convexity:
  • Applications in AI, Robotics
  • Factorization, structure \& sparsity
  • Libraries
  • Non-convexity

Students should bring solid knowledge of linear algebra and analysis, as well as good coding skills.

References

• Maths for Intelligent Systems script
• Boyd & Vandenberghe: Convex Optimization
• Nocedal & Wright: Numerical Optimization

Schedule, slides & exercises

date	topics	slides	exercises (due on 'date'+1)
Nov 3.	Introduction & Orga	01-introduction
Nov 10.	Unconstrained Optimization	02-unconstrainedOpt 02-functions	e00-mathsCheck e00-pythonCheck
Nov 17.	Unconstrained Optimization		e01-gradientDescent
Nov 24.	Constrained Optimization	03-constrainedOpt	e02-unconstrainedOpt
Dec 1.			e03-newtonMethods
Dec 8.			e04-constraints
Dec 15.	Convex Programs	04-convexProblems	e05-lagrange
Jan 5.			e06-primaldual
Jan 12.	Differentiable Optimization	05-differentiableOpt	e07-convexOpt
Jan 19.	Bound Constraints, Phase I, Restarts	06-boundsEtc	-cancelled-
Jan 26.	Global Optimization	07-globalBayesianOptimization	e08-ILPrelaxation
Feb 2.			e09-boundsRestarts
Feb 9.	Structure	08-structure	e10-gpBayesOpt dannysGP.py
Feb 16.			ExamPreparationExercises

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