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First a brief overview is given of Camillo Possio’s short but outstanding and fruitful career. This is followed by an outline of the state of the art in flutter and unsteady aerodynamic research, and the challenges and problems like high-speed flight that arose in aircraft development at that time. Possio’s first publications on gas dynamic and supersonic problems are reviewed. The main focus is on the 1938 report on unsteady subsonic compressible 2D flow that became famous and was named after him, because he was the first person to developed an unsteady compressible aerodynamic theory, which was urgently needed in those years. The theory, which is based on Prandtl’s acceleration potential is briefly outlined. Some discussions and comments that took place in Germany and other countries at that time highlight the importance of this work for the scientific community. Early solutions of Possio’s integral equation developed by himself and later ones developed by other researchers are presented, as well as approaches that extended the theory to 3 dimensional flows before the war, like Kuessner’s theory, which was probably influenced by Possio. Finally Camillo Possio’s later scientific contributions to wind tunnel interference and to hydrodynamics are described. A summary of some developments of the 2nd half of the 20th century demonstrate that Camillo Possio created a milestone for modern aircraft research during his very short career.

A central problem of AeroElasticity is the determination of the speed of the aircraft corresponding to the onset of an endemic instability known as wing ‘flutter’. Currently all the effort is completely computational: wedding Lagrangian NASTRAN codes to the CFD codes to produce ‘Time Marching’ solutions. While they have the ability to handle nonlinear complex geometry structures as well as viscous flow, they are based approximation of the p.d.e. by o.d.e., and restricted to specified numerical parameters. This limits generality of results and provides little insight into phenomena. And of course are inadequate for Control Design for stabilization. Retaining the continuum models,we can show that the basic problem is a Boundary Value/Control problem for a pair of coupled partial differential equations, and the composite problem can be cast as a nonlinear Convolution/Evolution equation in a Hilbert Space. The Flutter speed can then be characterized as Hopf Bifurcation point, and determined completely by the linearised equations. Solving the linearised equations is equivalent to solving a singular integral equation discovered by Possio in 1938 for oscillatory response.In this paper we examine the Equation and its generalizations from the modern mathematical control theory viewpoint.

A review of the papers written by Camillo Possio on Flight Dynamics and Hydrodynamics is presented. The scope of the note is to underline how the versatile young researcher succeeded in delivering interesting contributions to the engineering sciences that go beyond the renown equation that bears his name.

This paper recalls the work of D. Pompeiu who introduced the notion of set distance in his thesis published one century ago. The notion was further studied by F. Hausdorff, C. Kuratowski who acknowledged in their books the contribution of Pompeiu and it is frequently called the Hausdorff distance.

In the dynamical theory of granular matter, the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain Ω ⊂ R^2. The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge-Kantorovich problem, is the object of this paper. Our main result is an integral representation formula for the solution, in terms of the boundary curvature and of the normal distance to the cut locus of Ω.

An appealing feature of interior methods for linear programming is that the number of iterations required to solve a problem tends to be relatively insensitive to the choice of initial point. This feature has the drawback that it is difficult to design interior methods that efficiently utilize information from an optimal solution to a “nearby” problem. We discuss this feature in the context of general nonlinear programming and specialize to linear programming. We demonstrate that warm start for a particular nonlinear programming problem, given a near-optimal solution for a “nearby” problem, is closely related to an SQP method applied to an equality-constrained problem. These results are further refined for the case of linear programming.

A new active set algorithm (ASA) for large-scale box constrained optimization is introduced. The algorithm consists of a nonmonotone gradient projection step, an unconstrained optimization step, and a set of rules for switching between the two steps. Numerical experiments and comparisons are presented using box constrained problems in the CUTEr and MINPACK test problem libraries.

The paper describes and analyzes an application of the p-regularity theory to nonregular , ( irregular, degenerate ) nonlinear optimization problems. The p-regularity theory, also known as the factor-analysis of nonlinear mappings , has been developing successfully for the last twenty years. The p-factor-approach is based on the construction of a p-factor-operator, which allows us to describe and analyze nonlinear problems in the degenerate case. First, we illustrate how to use the p-factor-approach to solve degenerate optimization problems with equality constraints, in which the Lagrange multiplier associated with the objective function might be equal to zero. We then present necessary and sufficient optimality conditions for a degenerate optimization problem with inequality constraints. The p-factor-approach is also used for solving mathematical programs with equilibrium constraints (MPECs). We show that the constraints are 2-regular at the solution of the MPEC. This property allows us to localize the minimizer independently of the objective function. The same idea is applied to some other nonregular nonlinear programming problems and allows us to reduce these problems to a regular system of equations without an objective function.

Non monotone algorithms allow a possible increase of function values at certain iterations. This paper gives a suitable control on this increase to preserve the convergence properties of its monotone counterpart. A new efficient MultiLineal Search is also proposed for minimization algorithms.

The efficiency of the network flow techniques can be exploited in the solution of nonlinearly constrained network flow problems by means of approximate sub-gradient methods. In particular, we consider the case where the side constraints (non-network constraints) are convex. We propose to solve the dual problem by using ε -subgradient methods given that the dual function is estimated by minimizing approximately a Lagrangian function with only network constraints. Such Lagrangian function includes the side constraints. In order to evaluate the efficiency of these ε -subgradient methods some of them have been implemented and their performance computationally compared with that of other well-known codes. The results are encouraging.