KT-invexity in optimal control problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Optimality Conditions for D.C. Vector Optimization Problems under D.C. Constraints

2000 Mathematics Subject Classification: Primary 90C29; Secondary 49K30.

Nonsmooth continuous-time optimization problems: Necessary conditions

We consider Lipschitz continuous-time nonlinear optimization problems and provide first-order necessary optimality conditions of both Fritz John and Karush-Kuhn-Tucker types. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Optimality conditions for pareto nonsmooth nonconvex programming in banach spaces

In this paper, we consider a vector optimization problem where all functions involved are defined on Banach spaces. We obtain necessary and sufficient criteria for optimality in the form of Karush-Kuhn-Tucker conditions. We also introduce a nonsmooth dual problem and provide duality theorems.

Optimality conditions for infinite horizon control problems with state constraints

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Second Order Optimality Conditions in Nonsmooth Unconstrained Optimization

AMS subject classification: 49J52, 90C30.

Influence of lime type and curing conditions on lime and lime-metakaolin mortars

Durability of Building Materials and Components (Vasco Peixoto de de Freitas, J.M.P.Q. Delgado, eds.), Building Pathology and Rehabilitation, vol. 3, VIII, 105-126. ISBN: 978-3-642-37474-6 (Print) 978-3-642-37475-3 (Online). Springer-Verlag Berlin Heidelberg. DOI: 10.1007/978-3-642-37475-3_5

Generic optimality conditions for semi-algebraic convex programs

We consider linear optimization over a nonempty convex semi-algebraic feasible region F. Semidefinite programming is an example. If F is compact, then for almost every linear objective there is a unique optimal solution, lying on a unique \active" manifold, around which F is \partly smooth", and the second-order sufficient conditions hold. Perturbing the objective results in smooth variation of the optimal solution. The active manifold consists, locally, of these perturbed optimal solutions; it is independent of the representation of F, and is eventually identified by a variety of iterative algorithms such as proximal and projected gradient schemes. These results extend to unbounded sets F.

New optimality conditions for nonsmooth control problems

This work considers nonsmooth optimal control problems and provides two new sufficient conditions of optimality. The first condition involves the Lagrange multipliers while the second does not. We show that under the first new condition all processes satisfying the Pontryagin Maximum Principle (called MP-processes) are optimal. Conversely, we prove that optimal control problems in which every MP-process is optimal necessarily obey our first optimality condition. The second condition is more natural, but it is only applicable to normal problems and the converse holds just for smooth problems. Nevertheless, it is proved that for the class of normal smooth optimal control problems the two conditions are equivalent. Some examples illustrating the features of these sufficient concepts are presented. © 2012 Springer Science+Business Media New York.

Sufficient Second Order Optimality Conditions for C^1 Multiobjective Optimization Problems

2000 Mathematics Subject Classification: Primary 90C29; Secondary 90C30.

Calculus of Variations with Classical and Fractional Derivatives

MSC 2010: 49K05, 26A33

Novel developments in process optimisation using predictive control

In industrial practice, constrained steady state optimisation and predictive control are separate, albeit closely related functions within the control hierarchy. This paper presents a method which integrates predictive control with on-line optimisation with economic objectives. A receding horizon optimal control problem is formulated using linear state space models. This optimal control problem is very similar to the one presented in many predictive control formulations, but the main difference is that it includes in its formulation a general steady state objective depending on the magnitudes of manipulated and measured output variables. This steady state objective may include the standard quadratic regulatory objective, together with economic objectives which are often linear. Assuming that the system settles to a steady state operating point under receding horizon control, conditions are given for the satisfaction of the necessary optimality conditions of the steady-state optimisation problem. The method is based on adaptive linear state space models, which are obtained by using on-line identification techniques. The use of model adaptation is justified from a theoretical standpoint and its beneficial effects are shown in simulations. The method is tested with simulations of an industrial distillation column and a system of chemical reactors.

On the solution of mathematical programming problems with equilibrium constraints

Mathematical programming problems with equilibrium constraints (MPEC) are nonlinear programming problems where the constraints have a form that is analogous to first-order optimality conditions of constrained optimization. We prove that, under reasonable sufficient conditions, stationary points of the sum of squares of the constraints are feasible points of the MPEC. In usual formulations of MPEC all the feasible points are nonregular in the sense that they do not satisfy the Mangasarian-Fromovitz constraint qualification of nonlinear programming. Therefore, all the feasible points satisfy the classical Fritz-John necessary optimality conditions. In principle, this can cause serious difficulties for nonlinear programming algorithms applied to MPEC. However, we show that most feasible points do not satisfy a recently introduced stronger optimality condition for nonlinear programming. This is the reason why, in general, nonlinear programming algorithms are successful when applied to MPEC.

Condições de otimalidade para controle ótimo via formalismo de Dubovitskii-Milyutin

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Robust Image Registration with Global Intensity Transformation

This paper presents a registration method for images with global illumination variations. The method is based on a joint iterative optimization (geometric and photometric) of the L1 norm of the intensity error. Two strategies are compared to directly find the appropriate intensity transformation within each iteration: histogram specification and the solution obtained by analyzing the necessary optimality conditions. Such strategies reduce the search space of the joint optimization to that of the geometric transformation between the images.