Let $A=U|A|$ be the polar decomposition of an operator $A$ on a Hilbert space $mathscr{H}$ and $lambdain(0,1)$. The $lambda$-Aluthge transform of $A$ is defined by $tilde{A}_lambda:=|A|^lambda U|A|^{1-lambda}$. In this paper we show that emph{i}) when $mathscr{N}(|A|)=0$, $A$ is self-adjoint if and only if so is $tilde{A}_lambda$ for some $lambdaneq{1over2}$. Also $A$ is self adjoint if and onl...

A well–known problem in indirect optimal control is to find a suitable initial guess for the adjoint states which is sufficiently close to the optimal solution. This paper presents a new homotopy approach to overcome this problem by deriving an auxiliary optimal control problem (OCP) for which the adjoint states are simply zero. A continuation method is employed to smoothly reach the original O...

Adaptivity in space and time is ubiquitous in modern numerical simulations. The large number of unknowns associated with today’s typical inverse problem may run in the millions, or more. To capture small scale phenomena in regions of interest, adaptive mesh and temporal step refinements are required, since uniform refinements quickly make the problem computationally intractable. To date, there ...

Multi-adjoint logic programs has been recently introduced [9, 10] as a generalization of monotonic logic programs [2, 3], in that simultaneous use of several implications in the rules and rather general connectives in the bodies are allowed. This paper discusses abductive reasoning—that is, reasoning in which explanatory hypotheses are formed and evaluated. To model uncertainty in human cogniti...

This paper presents a generalization of the minimax state estimation approach for singular linear Differential-Algebraic Equations (DAE) with uncertain but bounded input and observation’s noise. We apply generalized Kalman Duality principle to DAE in order to represent the minimax estimate as a solution of a dual control problem for adjoint DAE. The latter is then solved converting the adjoint ...

In this paper, the optimal control problem of the stationary Navier-Stokes equations in the presence of state constraints is investigated. We prove the existence of an optimal solution and derive first order necessary optimality conditions. The regularity of the adjoint state and the state constraint multiplier is also studied. Finally, the Lipschitz stability of the optimal control, state and ...

We consider the resolution of an inverse problem for the identification of some reduced nonlinear diffusive models. The modal identification method is dealt with along with a gradient-type optimization method. Two distinct approaches are considered and compared. On one hand the classical finite differences approach and, on the other hand, the adjoint method for the computation of the objective ...

Adjoints are used in optimization to speed-up computations, simplify optimality conditions or compute sensitivities. Because time is reversed in adjoint equations with first order time derivatives, boundary conditions and transmission conditions through shocks can be difficult to understand. In this article we analyze the adjoint equations that arise in the context of compressible flows governe...

In this paper we present a method for estimating unknown parameters that appear on an avascular, spheric tumour growth model. The model for the tumour is based on nutrient driven growth of a continuum of live cells, whose birth and death generate volume changes described by a velocity field. The model consists on a coupled system of partial differential equations whose spatial domain is the tum...

In this paper, we consider the problem of identifying, by means of boundary element methods and nonlinear optimization, a cavity or obstacle of unknown location and shape embedded in a linearly acoustic or elastic medium. The unknown shape is classically sought as to achieve a best fit between the measured and computed values of some physical quantity, which is here the scattered acoustic press...