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Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane

Yuri L. Sachkov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized. Lower and upper bounds on the first conjugate time are proved. The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete symmetries of the exponential mapping. Optimal synthesis on an open dense subset of the state space is described.

Conservation law constrained optimization based upon front-tracking

Martin Gugat, Michaël Herty, Axel Klar, Gunter Leugering (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider models based on conservation laws. For the optimization of such systems, a sensitivity analysis is essential to determine how changes in the decision variables influence the objective function. Here we study the sensitivity with respect to the initial data of objective functions that depend upon the solution of Riemann problems with piecewise linear flux functions. We present representations for the one–sided directional derivatives of the objective functions. The results can be used...

Conservation law constrained optimization based upon Front-Tracking

Martin Gugat, Michaël Herty, Axel Klar, Gunter Leugering (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider models based on conservation laws. For the optimization of such systems, a sensitivity analysis is essential to determine how changes in the decision variables influence the objective function. Here we study the sensitivity with respect to the initial data of objective functions that depend upon the solution of Riemann problems with piecewise linear flux functions. We present representations for the one–sided directional derivatives of the objective functions. The results can be used...

Constant selections and minimax inequalities

Mircea Balaj (2006)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we establish two constant selection theorems for a map whose dual is upper or lower semicontinuous. As applications, matching theorems, analytic alternatives, and minimax inequalities are obtained.

Constrained optimization: A general tolerance approach

Tomáš Roubíček (1990)

Aplikace matematiky

To overcome the somewhat artificial difficulties in classical optimization theory concerning the existence and stability of minimizers, a new setting of constrained optimization problems (called problems with tolerance) is proposed using given proximity structures to define the neighbourhoods of sets. The infimum and the so-called minimizing filter are then defined by means of level sets created by these neighbourhoods, which also reflects the engineering approach to constrained optimization problems....

Contact between elastic bodies. I. Continuous problems

Jaroslav Haslinger, Ivan Hlaváček (1980)

Aplikace matematiky

Problems of a unilateral contact between bounded bodies without friction are considered within the range of two-dimensional linear elastostatics. Two classes of problems are distinguished: those with a bounded contact zone and with an enlargign contact zone. Both classes can be formulated in terms of displacements by means of a variational inequality. The proofs of existence of a solution are presented and the uniqueness discussed.

Contact between elastic bodies. II. Finite element analysis

Jaroslav Haslinger, Ivan Hlaváček (1981)

Aplikace matematiky

The paper deals with the approximation of contact problems of two elastic bodies by finite element method. Using piecewise linear finite elements, some error estimates are derived, assuming that the exact solution is sufficiently smooth. If the solution is not regular, the convergence itself is proven. This analysis is given for two types of contact problems: with a bounded contact zone and with enlarging contact zone.

Continuity of solutions to a basic problem in the calculus of variations

Francis Clarke (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We study the problem of minimizing ∫ Ω F ( D u ( x ) ) d x over the functions u ∈ W 1 , 1 ( Ω ) that assume given boundary values φ on Γ : = ∂ Ω . The lagrangian F and the domain Ω are assumed convex. A new type of hypothesis on the boundary function φ is introduced: thelower (or upper) bounded slope condition. This condition, which is less restrictive than the familiar bounded slope condition of Hartman, Nirenberg and Stampacchia, allows us to extend the classical Hilbert-Haar regularity theory to the case of semiconvex (or semiconcave) boundary...

Continuity of the non-convex play operator in the space of rectifiable curves

Jana Kopfová, Vincenzo Recupero (2023)

Applications of Mathematics

We prove that the vector play operator with a uniformly prox-regular characteristic set of constraints is continuous with respect to the B V -norm and to the B V -strict metric in the space of rectifiable curves, i.e., in the space of continuous functions of bounded variation. We do not assume any further regularity of the characteristic set. We also prove that the non-convex play operator is rate independent.

Control for the Sine-Gordon equation

Madalina Petcu, Roger Temam (2004)

ESAIM: Control, Optimisation and Calculus of Variations

In this article we apply the optimal and the robust control theory to the sine-Gordon equation. In our case the control is given by the boundary conditions and we work in a finite time horizon. We present at the beginning the optimal control problem and we derive a necessary condition of optimality and we continue by formulating a robust control problem for which existence and uniqueness of solutions are derived.

Currently displaying 61 – 80 of 147