Osion kuvaus

• Yleinen

• Introduction to the course that intends to answer the question what you should expect from the course and what you shouldn't.

• Basics fact of linear algebra and matrix computations used throughout the course of convex optimization.

•  subspace, affine set, convex set, convex cone

 simple examples and properties

 combination and hulls

 ellipsoids, polyhedra, norm balls

 affine and projective transformations

 separating hyperplanes

 generalized inequalities

•  convex functions, epigraph

 simple examples, elementary properties

 more examples, more properties

 Jensen's inequality

 quasiconvex, quasiconcave functions

 log-convex and log-concave functions

 K-convexity

•  abstract form problem

 standard form problem

 convex optimization problem

 standard form with generalized inequalities

 mulitcriterion optimization

 restriction and relaxation

• • linear programming

• examples and applications

• linear fractional programming

programming

• examples and applications

• Semidefinite programming

• applications

• CVX is a modeling system for disciplined convex programming. It will be explained how to use it.

• · terminology

· general descent method

· line search types

· steepest descent method

· Newton's method

• brief history of SUMT & IP methods

· logarithmic barrier function

· central path

· basic SUMT

• Lecture on Sept. 15, 2021

• Lecture on Sept. 22, 2021

• Lecture on Sept. 29, 2021

Because the Aalto network was down during the lecture, the beginning of the lecture was lost.

• Lecture on Oct. 6, 2021

• Homework 1: Convex Sets

• Lecture on Oct. 13, 2021

• Lecture on Oct. 20, 2021

• Lecture on Oct. 27, 2021

• Homework 2: Convex Functions

• Lecture on Nov. 3, 2021

• Lecture on Nov. 10, 2021

• Homework 3: Optimization Problems

• Lecture on Nov. 17 2021

• Lecture on Nov. 24 2021

• Lecture on Dec. 1, 2021

• Lecture on Dec. 8, 2021
• Homework 1 Solutions of analytic problems

• Homework 2 Solutions of analytic problems

• Homework 3 Solutions of analytic problems

• Exam over zoom

• Beginning of the exam on Dec. 15