11 citations · 15 across the 17 of their papers we have counts for
11 papers · 1 filter
Inverse quasiconvexification
Pablo Pedregal
In the context of the Calculus of Variations for non-convex, vector variational problems, the natural process of going from a function to its quasiconvexification is quite…
Morrey's conjecture: rank-one convexity implies quasi-convexity for two-dimensional, two-component maps
Pablo Pedregal
We prove that for two-component maps in dimension two, rank-one convexity is equivalent to quasiconvexity. The essential tool for the proof is a fixed-point argument for a suitable…
On a variant of Tykhonov regularization in optimal control under PDEs
Pablo Pedregal
We make some remarks on a variant of the classical Tikhonov regularization in optimal control under PDEs which allows for a certain flexibility in dealing with non-linearities and…
About least-squares type approach to address direct and controllability problems
Arnaud Münch, Pablo Pedregal
- We discuss the approximation of distributed null controls for partial differential equations. The main purpose is to determine an approximation of controls that drives the soluti…
Constrained optimization through fixed point techniques
Pablo Pedregal
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstraine…
Some evidence in favor of Morrey's conjecture
Pablo Pedregal
We provide further evidence to favor the fact that rank-one convexity does not imply quasiconvexity for two-component maps in dimension two. We provide an explicit family of maps p…
Weak limits in non-linear conductivity
Pablo Pedregal
The problem of characterizing weak limits of sequences of solutions for a non-linear diffusion equation of -laplacian type is addressed. It is formulated in terms of certain mom…
Existence results for optimal control problems with some special non-linear dependence on state and control
Pablo Pedregal, Jorge Tiago
We present a general approach to prove existence of solutions for optimal control problems not based on typical convexity conditions which quite often are very hard, if not impossi…
A different look at controllability
Pablo Pedregal
We explore further controllability problems through a standard least square approach. By setting up a suitable error functional , and putting for the infimum, we inter…
Optimal feedback control, linear first-order PDE systems, and obstacle problems
Pablo Pedregal
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control probl…
A dynamical-system approach to mathematical programming
Pablo Pedregal
We explore how to build a vector field from the various functions involved in a given mathematical program, and show that locally-stable equilibria of the underlying dynamical syst…