Sumários

Two kinds of problems solved with Convex Analysis

22 Maio 2019, 15:30 • José Francisco da Silva Costa Rodrigues

Application of duality in two variational problems solvable with convex analysis tools; relations and explicit forms of the primal and dual problems:

1- Problems with discontinuities in the gradient  (Mossolov-Miasnikov's problem and the least-plastic torsion problem) — exposition by Francisco Agostinho;
2- A problem of fourth order with a nonlocal term in a non reflexive Banach space (Berkowitz and Pollard's filtering problem) — exposition by Lara Luhrmann.

Lectures the 23rd May, from 16:30-19:30.

Duality by the Minimax theorem

16 Maio 2019, 14:30 • José Francisco da Silva Costa Rodrigues

General relation of saddle points with the equity relation of MaxInf with Min Sup of Lagrangians. Characterisation of saddle points for partially Gâteaux-differential Lagrangians under convexity assumptions and relation with variational inequalities. Sufficient conditions of saddle points in reflexive Banach spaces. Applications of saddle points method to duality. The case of equilibrium of an elastic body on a rigid base—comparison of the approach in Ekeland-Téman (pp. 218-221) Nad in Duvaut-Lions (pp. 121-123).


Lecture: Friday 18 at 14:00-16:30 room 6.2.33

Duality by the Minimax theorem

15 Maio 2019, 17:00 • José Francisco da Silva Costa Rodrigues

General relation of saddle points with the equality relation of Max-Inf with Min-Sup of Lagrangians. Characterisation of saddle points for partially Gâteaux-differentiable Lagrangians under convexity assumptions and relation with variational inequalities. Sufficient conditions of saddle points in reflexive Banach spaces. Applications of saddle points method to duality. The case of equilibrium of an elastic body on a rigid base—comparison of the approach in Ekeland-Témam (pp. 218-221) and in Duvaut-Lions (pp. 121-123).


Lecture: Friday 18 at 14:00-16:30 room 6.2.33

Duality by the Minimax theorem

15 Maio 2019, 15:30 • José Francisco da Silva Costa Rodrigues

General relation of saddle points with the equity relation of MaxInf with Min Sup of Lagrangians. Characterisation of saddle points for partially Gâteaux-differential Lagrangians under convexity assumptions and relation with variational inequalities. Sufficient conditions of saddle points in reflexive Banach spaces. Applications of saddle points method to duality. The case of equilibrium of an elastic body on a rigid base—comparison of the approach in Ekeland-Téman (pp. 218-221) Nad in Duvaut-Lions (pp. 121-123).


Lecture: Friday 18 at 14:00-16:30 room 6.2.33

9 Maio 2019, 14:30 • José Francisco da Silva Costa Rodrigues

Lagrangian and Saddle Points —relations with the primal and with the dual problems in the case of stable and normal assumptions; the case of reflexive Banach spaces.

The important special cases of primal and dual problems in ordered spaces under inequality constraints: the general abstract case; the specific form of the Lagrangian; the Kuhn-Tucker conditions in R^N;  the case of variational inequalities.
The bridal problem and generalised solutions.

Applied topics to be developed:
— non-differential functionals of the gradient— Bingham flow (special steady case) and the least-plastic torsion problem;
— non-differential functional in a nonlocal case — a problem in filtering theory;
— a non reflexive case— non-parametric minimal surfaces.

The course took place from 16:15—19:00, the 9 May.