This page describes the 60 hour course given at University ParisSaclay in the M2 Optimization, during the academic year 20182019, entitled Advanced
Continuous Optimization. It contains
 the teacher internet pages,
 a short presentation of its contents,
 the detailed program of part I, part II, and part III.
The second part of the module (20 hours) focuses on the implementation of some of the previously seen algorithms in Matlab and allows the designer to understand its behavior and to evaluate its efficiency on a concrete problem. A choice will have to be made between the following two projects: (i) the implementation of an SQP solver to solve the hanging chain problem (viewed as a nonlinear optimization problem) or (ii) the implementation of a selfdual conic optimization (SDCO) solver in real numbers to solve various academic/concrete problems, such as the global minimization of a univariate polynomial or a few small size OPF problems (more precisely the rank relaxation of a QCQP version of this problem).
The last part of the module is a 10 hour lecture given by Claudia Sagastizábal (Unicamp, Brazil).
Postlecture notes (the access to some notes requires the username "Student" and the given password)
Monday September 17 2018 
Presentation and recalls 
Presentation of the course Background

Monday September 24 2018 
First order optimality conditions of a general optimization problem 
Background

Monday October 1 2018 
Second order optimality conditions for the equality and inequality constrained problem 
Background

Monday October 8 2018 
JosephyNewton algorithm for solving functional inclusions 
Background

Monday October 15 2018 
The SQP algorithm for solving the equality and inequality constrained problem 
Background

Monday October 22 2018 
The semismooth Newton algorithm for solving nonsmooth nonlinear equations 
Linearization methods

Monday November 5 2018 
Semidefinite optimization 
Background

Monday November 12 2018 
Examination

The goal of this course is to guide the student in the implementation of some well known optimization algorithms and in its use to solve a concrete problem. The student will choose among the following two projects.
Actual program on a daily basis
Monday November 19 2018 
Problem modeling and simulator design (20112018)  Directions of displacement  
Monday November 26 2018 
The local SQP algorithm (26112018)  A feasible predictorcorrector algorithm  
Monday December 3 2018 
Globalization by linesearch (3122018)  Finding an appropriate starting point  
Monday December 10 2018 
QuasiNewton version (10122018)  Starting from an infeasible point  
Monday December 17 2018 
Lecture notes (19122018)  
Monday January 7 2019 
Oral examination
On the examination (19122018)

Oral examination
On the examination (19122018)

A VU point of view of nonsmooth optimizationat ENSTA Paristech, Palaiseau, on
Summary of the Lecture
The realization that many nondifferentiable functions exhibit some form of structured nonsmoothness has been attracting the efforts of many researchers in the last decades. Identifying theoretically and computationally certain manifolds where a nonsmooth function behaves smoothly poses challenges for the nonsmooth optimization community. We review a sequence of milestones in the area that led to the development of algorithms of the bundle type that can track the region of smoothness and mimic a Newton algorithm to converge with superlinear speed. The new generation of bundle methods is sufficiently versatile to deal with structured objective functions, even when the available information is inexact.
Examination
Make a report of a few pages explaining what you have understood (and possibliy learned) from the lectures.
Deadline: Sunday 27th of January, 12 pm.