An Extremal Problem Involving Functions and Their Inverses.
An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...
An hp-Discontinuous Galerkin Method for the Optimal Control Problem of Laser Surface Hardening of Steel
In this paper, we discuss an hp-discontinuous Galerkin finite element method (hp-DGFEM) for the laser surface hardening of steel, which is a constrained optimal control problem governed by a system of differential equations, consisting of an ordinary differential equation for austenite formation and a semi-linear parabolic differential equation for temperature evolution. The space discretization of the state variable is done using an hp-DGFEM, time and control discretizations are based on a discontinuous Galerkin...
An idempotent algorithm for a class of network-disruption games
A game is considered where the communication network of the first player is explicitly modelled. The second player may induce delays in this network, while the first player may counteract such actions. Costs are modelled through expectations over idempotent probability measures. The idempotent probabilities are conditioned by observational data, the arrival of which may have been delayed along the communication network. This induces a game where the state space consists of the network delays. Even...
An ill-posed nonlocal two-point problem for systems of partial differential equations.
An imbedding theorem in the calculus of variations for multiple integrals, addendum.
An implementation of recursive quadratic programming variable metric methods for linearly constrained nonlinear minimax approximation
An implicit extragradient method for hierarchical variational inequalities.
An implicit hierarchical fixed-point approach to general variational inequalities in Hilbert spaces.
An implicit iterative scheme for an infinite countable family of asymptotically nonexpansive mappings in Banach spaces.
An implicit-function theorem for a class of monotone generalized equations
An improved convergence analysis of a superquadratic method for solving generalized equations.
An impulsive control problem with state constraint
An index formula for the degree of (S)-mappings associated with one-dimensional -Laplacian.
An inexact proximal-type method for the generalized variational inequality in Banach spaces.
An instantaneous semi-Lagrangian approach for boundary control of a melting problem
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions...
An integrodifferential approach to modeling, control, state estimation and optimization for heat transfer systems
In this paper, control-oriented modeling approaches are presented for distributed parameter systems. These systems, which are in the focus of this contribution, are assumed to be described by suitable partial differential equations. They arise naturally during the modeling of dynamic heat transfer processes. The presented approaches aim at developing finitedimensional system descriptions for the design of various open-loop, closed-loop, and optimal control strategies as well as state, disturbance,...
An intermediate existence theory in the calculus of variations
An interpolatory estimate for the UMD-valued directional Haar projection [Book]
An intersection theorem for set-valued mappings
Given a nonempty convex set in a locally convex Hausdorff topological vector space, a nonempty set and two set-valued mappings , we prove that under suitable conditions one can find an which is simultaneously a fixed point for and a common point for the family of values of . Applying our intersection theorem we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.