Directional lipschitzian optimal solutions and directional derivative for the optimal value function in nonlinear mathematical programming
Discrete dynamic programming and viscosity solutions of the Bellman equation
Discrete mechanics and optimal control: An analysis
The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper...
Discrete mechanics and optimal control: An analysis*
The optimal control of a mechanical system is of crucial importance in many application areas. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion sequences in robotics and biomechanics. In most cases, some sort of discretization of the original, infinite-dimensional optimization problem has to be performed in order to make the problem amenable to computations. The approach proposed in this paper...
Discrete optimal control problems with nonsmooth costs
Discrete periodic geodesics in a surface.
Duality based a posteriori error estimates for higher order variational inequalities with power growth functionals.
Duality theory in mathematical programming and optimal control
Dual-weighted goal-oriented adaptive finite elements for optimal control of elliptic variational inequalities
A dual-weighted residual approach for goal-oriented adaptive finite elements for a class of optimal control problems for elliptic variational inequalities is studied. The development is based on the concept of C-stationarity. The overall error representation depends on primal residuals weighted by approximate dual quantities and vice versa as well as various complementarity mismatch errors. Also, a priori bounds for C-stationary points and associated multipliers are derived. Details on the numerical...
Dykstra's algorithm as the nonlinear extension of Bregman's optimization method.
Dynamic optimal cooling control for continuous casting of steel
Efficient algorithm to solve optimal boundary control problem for Burgers' equation
In this paper, we propose a novel algorithm for solving an optimal boundary control problem of the Burgers' equation. The solving method is based on the transformation of the original problem into a homogeneous boundary conditions problem. This transforms the original problem into an optimal distributed control problem. The modal expansion technique is applied to the distributed control problem of the Burgers' equation to generate a low-dimensional dynamical system. The control parametrization method...
El contraste de hipótesis compuesta frente a alternativa simple como problema de programación matemática infinita.
Embedding variational inequalities and their generalizations into a separation scheme.
Empirical regression quantile processes
We address the problem of estimating quantile-based statistical functionals, when the measured or controlled entities depend on exogenous variables which are not under our control. As a suitable tool we propose the empirical process of the average regression quantiles. It partially masks the effect of covariates and has other properties convenient for applications, e.g. for coherent risk measures of various types in the situations with covariates.
Error analysis of discrete approximations to bang-bang optimal control problems: the linear case
Error estimates and free-boundary convergence for a finite difference discretization of a parabolic variational inequality
Error estimates for finite element approximations of elliptic control problems
We investigate finite element approximations of one-dimensional elliptic control problems. For semidiscretizations and full discretizations with piecewise constant controls we derive error estimates in the maximum norm.
Error estimates for the finite element approximation of a semilinear elliptic control problem with state constraints and finite dimensional control space
The finite element approximation of optimal control problems for semilinear elliptic partial differential equation is considered, where the control belongs to a finite-dimensional set and state constraints are given in finitely many points of the domain. Under the standard linear independency condition on the active gradients and a strong second-order sufficient optimality condition, optimal error estimates are derived for locally optimal controls.
Error estimates for the finite element discretization of semi-infinite elliptic optimal control problems
In this paper we derive a priori error estimates for linear-quadratic elliptic optimal control problems with finite dimensional control space and state constraints in the whole domain, which can be written as semi-infinite optimization problems. Numerical experiments are conducted to ilustrate our theory.