Time: 9:00 – 12:00, March 2 and March 10, 2015

Location: VIASM Lecture Hall C2

Lecturer: Marc Lassonde (Mathematics and Informatics Department, Université des Antilles et de la Guyane)

Professor Marc Lassonde, a well-known expert in Variational Analysis and Optimization Theory, will present a minicourse on Variational Analysis and Applications at Vietnam Institute for Advanced Study in Mathematics in the mornings of March 2 (Monday) and March 10 (Tuesday), 2015.

1. March 2 (Monday), 9:00 – 12:00 (two lectures + a 20-minute coffee break)
Lecture title: Introduction to Monotonicity

Contents:

1/ The Minty-Browder “monotonicity method” for the solutions of nonlinear equations in Banach spaces.

2/ Minty surjectivity theorems, proximal algorithm and variational inequalities

3/ Maximal monotone operators

3.1/ Examples:
- convex subdifferential and duality mapping
- hemicontinuous monotone operators
- skew linear operators
- the Laplacian

3.2/ Properties:
- local boundedness
- minimal cuscos
- sum theorems

4/ Generalized monotonicity

2. March 10 (Monday), 9:00 – 12:00 (two 80-minutes lectures + a 20-minute coffee break)
Lecture title: Introduction to Subdifferentials

Contents:

1/ Backgroung: bornologies and differentiability

2/ Selected subdifferentials
- Moreau-Rockafellar or convex subdifferential
- proximal subdifferential
- bornological subdifferentials (Fréchet, Hadamard, Gateaux)
- Clarke and Michel-Penot subdidifferentials
- Ioffe subdifferential
- abstract subdifferential

3/ Variational principles and Separation Principle

4/ Qualication conditions and sum of subdifferentials

5/ Calculus without qualication conditions

Interested researchers, master students, and PhD students are cordially invited to attend the minicourse.

No registration is needed.

Contact person: Prof. Nguyen Dong Yen (Mobile phone: 01287246945)