Thursday, 13:15 - 13:40 h, Room: MA 415

 

Francisco José Silva Alvarez
Characterization of quadratic growth for strong minima in the optimal control of semi-linear elliptic equations

Coauthors: Terence Bayen, Frédéric Bonnans

 

Abstract:
In this work, we are concerned with the following optimal control problem:


minu J(u) := ∫Ω l(x,yu(x),u(x)) d x,


under bounds constraints on the control u, and where yu is the unique solution of


\begin{cases}
 -Δ y(x) + \varphi(x,y(x),u(x)) = 0,  \mathrm{for}  x ∈ Ω,\
\hspace{3.75cm} y(x) = 0, \hspace{0.12cm} \mathrm{for}  x ∈ \partial Ω.
\end{cases}


We extend to strong solutions classical second order analysis results, which are usually established for weak solutions. We mean by strong solution a control \bar{u} that satisfies:


There exists ε>0 such that J(\bar{u) ≤ J(u) for all u with || yu-y\bar{u}|| ≤ ε.}


The study of strong solutions, classical in the Calculus of Variations, seems to be new in the context of the optimization of elliptic equations. Our main result is a characterization of local quadratic growth for the cost function J around a strong minimum.

 

Talk 1 of the invited session Thu.2.MA 415
"Theory and methods for PDE-constrained optimization problems with inequalities" [...]
Cluster 19
"PDE-constrained optimization & multi-level/multi-grid methods" [...]

 

  There are three major facts that should be watched out for in all payday loans in the United States. Therefore, we can say that the active substances in its composition are more perfectly mixed. Vardenafil is not only present in the original Levitra, but also as part of its analogs.