Optimal Shape Design Subject to Elliptic Variational Inequalities

Iterations for Elliptic Variational Inequalities

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non{diierentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constra...

Monotone Iterations for Elliptic Variational Inequalities

A wide range of free boundary problems occurring in engineering and industry can be rewritten as a minimization problem for a strictly convex, piecewise smooth but non–differentiable energy functional. The fast solution of related discretized problems is a very delicate question, because usual Newton techniques cannot be applied. We propose a new approach based on convex minimization and constr...

Optimal Control of Variational Inequalities

We consider control problems for the variational inequality describing a single degree of freedom elasto-plastic oscillator. We are particularly interested in finding the ”critical excitation”, i.e., the lowest energy input excitation that drives the system between the prescribed initial and final states within a given time span. This is a control problem for a state evolution described by a va...

On a Convex Combination of Solutions to Elliptic Variational Inequalities

Let ugi the unique solutions of an elliptic variational inequality with second member gi (i = 1, 2). We establish necessary and sufficient conditions for the convex combination tug1 + (1 − t)ug2 , to be equal to the unique solution of the same elliptic variational inequality with second member tg1 + (1− t)g2. We also give some examples where this property is valid.

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)