Results 1  10
of
21
Analysis of Inexact TrustRegion InteriorPoint SQP Algorithms
, 1995
"... In this paper we analyze inexact trustregion interiorpoint (TRIP) sequential quadratic programming (SQP) algorithms for the solution of optimization problems with nonlinear equality constraints and simple bound constraints on some of the variables. Such problems arise in many engineering applicati ..."
Abstract

Cited by 11 (7 self)
 Add to MetaCart
In this paper we analyze inexact trustregion interiorpoint (TRIP) sequential quadratic programming (SQP) algorithms for the solution of optimization problems with nonlinear equality constraints and simple bound constraints on some of the variables. Such problems arise in many engineering applications, in particular in optimal control problems with bounds on the control. The nonlinear constraints often come from the discretization of partial differential equations. In such cases the calculation of derivative information and the solution of linearized equations is expensive. Often, the solution of linear systems and derivatives are computed inexactly yielding nonzero residuals. This paper analyzes the effect of the inexactness onto the convergence of TRIP SQP and gives practical rules to control the size of the residuals of these inexact calculations. It is shown that if the size of the residuals is of the order of both the size of the constraints and the trustregion radius, t...
Second Order Methods For Optimal Control Of TimeDependent Fluid Flow
, 1999
"... Second order methods for open loop optimal control problems governed by the twodimensional instationary NavierStokes equations are investigated. Optimality systems based on a Lagrangian formulation and adjoint equations are derived. The Newton and quasiNewton methods as well as various variants o ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
Second order methods for open loop optimal control problems governed by the twodimensional instationary NavierStokes equations are investigated. Optimality systems based on a Lagrangian formulation and adjoint equations are derived. The Newton and quasiNewton methods as well as various variants of SQPmethods are developed for applications to optimal ow control and their complexity in terms of system solves is discussed. Local convergence and rate of convergence are proved. A numerical example illustrates the feasibility of solving optimal control problems for twodimensional instationary NavierStokes equations by second order numerical methods in a standard workstation environment. Previously such problems were solved by gradient type methods.
Optimality Conditions And Generalized BangBang Principle For A StateConstrained Semilinear Parabolic Problem
 Numerical Functional Analysis and Optimization
, 1996
"... We consider a distributed optimal control problem governed by a semilinear parabolic equation, where constraints on the control and on the state are given. Aiming to show the existence of regular Lagrange multipliers we follow a linearization approach together with a twonorm technique. The theory i ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We consider a distributed optimal control problem governed by a semilinear parabolic equation, where constraints on the control and on the state are given. Aiming to show the existence of regular Lagrange multipliers we follow a linearization approach together with a twonorm technique. The theory is applied to derive a generalized bangbang principle. 1 This work was supported by EEC, HCM Contract CHRXCT940471 1. INTRODUCTION In this paper we investigate some optimal control problems where the state equation is a semilinear parabolic equation. In addition, we consider constraints on both the control and the state. Our main purpose is to get some Lagrange multipliers (for the stateequation) as regular as possible. Nonlinear problems usually involve smooth data. The general duality theory for the mathematical programming in Banach spaces provides Lagrange multipliers in dual spaces. The smoother the spaces for the data, the larger the dual spaces are. This means that, even if we ...
Modeling And Minimization Of Extinction In VolterraLotka Type Equations With Free Boundaries
, 1996
"... An equation of the distributed VolterraLotka type, with free boundary of the obstacle type, with possible applications in ecology, when extinction of the biological species is of particular concern, is introduced and solved. Optimal control problem for such an equation, and in particular the proble ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
An equation of the distributed VolterraLotka type, with free boundary of the obstacle type, with possible applications in ecology, when extinction of the biological species is of particular concern, is introduced and solved. Optimal control problem for such an equation, and in particular the problem of minimization of the area of extinction of the species, is introduced and to some extent solved. 1 Introduction Modeling of distributed population dynamics was studied in the literature (see [14] and the references given there). The optimal control of distributed population dynamics, by the method of monotone iterations 1 , was introduced by the author and others in [17, 8, 9] 2 . The crucial assumption in those studies is that the harvesting rate of the species is linear with respect to the size of the population. The consequence of such an assumption in a model is that the species is either totally extinct, or its density is strictly positive in all of the considered region. The p...
Numerical Methods for Nonlinear Inverse Problems
, 1996
"... Inverse problems of distributed parameter systems with applications to optimal control and identification are considered. Numerical methods and their numerical analysis for solving this kind of inverse problems are presented, main emphasis being on the estimates of the rate of convergence for variou ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Inverse problems of distributed parameter systems with applications to optimal control and identification are considered. Numerical methods and their numerical analysis for solving this kind of inverse problems are presented, main emphasis being on the estimates of the rate of convergence for various schemes. Finally, based on the given error estimates, a twogrid method and related algorithms are introduced, which can be used to solve nonlinear inverse problems effectively. 1 Introduction and preliminaries We consider inverse problems of distributed parameter systems, their numerical approximation with the finite element method, and, especially, introduce estimates of the rate of convergence for inverse identification and optimal control problems. In many applications, inverse problems can be nonlinear and illposed which makes them difficult to solve numerically. The parametertoobservation mapping is often nonlinear and not invertible. Here, University of Jyvaskyla, Department ...
SUMMARY
"... Inverse design of directional solidi cation processes in the presence of a strong external magnetic eld ..."
Abstract
 Add to MetaCart
Inverse design of directional solidi cation processes in the presence of a strong external magnetic eld
SYMMETRIC ERROR ESTIMATES FOR DISCONTINUOUS GALERKIN APPROXIMATIONS FOR AN OPTIMAL CONTROL PROBLEM ASSOCIATED TO SEMILINEAR PARABOLIC PDE’S
"... (Communicated by Jie Shen) Abstract. A discontinuous Galerkin finite element method for an optimal control problem having states constrained to semilinear parabolic PDE’s is examined. The schemes under consideration are discontinuous in time but conforming in space. It is shown that under suitable a ..."
Abstract
 Add to MetaCart
(Communicated by Jie Shen) Abstract. A discontinuous Galerkin finite element method for an optimal control problem having states constrained to semilinear parabolic PDE’s is examined. The schemes under consideration are discontinuous in time but conforming in space. It is shown that under suitable assumptions, the error estimates of the corresponding optimality system are of the same order to the standard linear (uncontrolled) parabolic problem. These estimates have symmetric structure and are also applicable for higher order elements.
Derivative Computations for a Class of Optimal Control Problems
, 1998
"... This paper addresses the computation of first and second order derivatives for a class of optimal control problems by the sensitivity and adjoint equation methods. The issues considered are the relationships between the derivative structure of the full and the reduced formulations and the properties ..."
Abstract
 Add to MetaCart
This paper addresses the computation of first and second order derivatives for a class of optimal control problems by the sensitivity and adjoint equation methods. The issues considered are the relationships between the derivative structure of the full and the reduced formulations and the properties of the nullspace basis operator associated with the linearized state equation. Keywords. optimal control, nonlinear optimization, adjoints, sensitivities AMS subject classifications. 49M37, 90C06, 90C30 1 Introduction In this paper we analyze the derivative structure of problems of the form minimize f(y; u) subject to c(y; u) = 0; (1) arising in optimal control. Here u represents the control, y represents the state, and c(y; u) = 0 represents the state equation. Often, y and u belong to a function space such as the Sobolev space H 1 or the space L 2 , and the state equation is a differential equation in y. Examples of optimal control problems of the form (1) are given, e.g., in [2...