共查询到20条相似文献,搜索用时 109 毫秒
1.
E. M. Rudoy 《Siberian Mathematical Journal》2009,50(2):341-354
We study a fourth-order elliptic equation in a domain with a curvilinear cut. There are unilateral constraints for the solution on the cut. Considering rather general sufficiently smooth perturbations of the domain, we study the asymptotics of the energy functional. We deduce a formula for the derivative of the energy functional with respect to the perturbation parameter of the domain. 相似文献
2.
In Ref. 1, Heideman and Levy developed the sequential conjugate-gradient-restoration algorithm for minimizing a functional subject to differential constraints and terminal constraints. In this report, several numerical examples are presented, some pertaining to a quadratic functional subject to linear constraints and some pertaining to a nonquadratic functional subject to nonlinear constraints. These examples demonstrate the feasibility as well as the rapid convergence characteristic of the sequential conjugate-gradient-restoration algorithm. 相似文献
3.
W. Wollner 《Computational Optimization and Applications》2010,47(1):133-159
In this paper we are concerned with a posteriori error estimates for the solution of some state constraint optimization problem
subject to an elliptic PDE. The solution is obtained using an interior point method combined with a finite element method
for the discretization of the problem. We will derive separate estimates for the error in the cost functional introduced by
the interior point parameter and by the discretization of the problem. Finally we show numerical examples to illustrate the
findings for pointwise state constraints and pointwise constraints on the gradient of the state. 相似文献
4.
Robert G. Jeroslow 《Mathematical Programming》1983,27(2):144-154
We study infinite sets of convex functional constraints, with possibly a set constraint, under general background hypotheses
which require closed functions and a closed set, but otherwise do not require a Slater point. For example, when the set constraint
is not present, only the consistency of the conditions is needed.
We provide hypotheses, which are necessary as well as sufficient, for the overall set of constraints to have the property
that there is no gap in Lagrangean duality for every convex objective function defined on ℝn. The sums considered for our Lagrangean dual are those involving only finitely many nonzero multipliers.
In particular, we recover the usual sufficient condition when only finitely many functional constraints are present. We show
that a certain compactness condition in function space plays the role of finiteness, when there are an infinite number of
functional constraints.
The author's research has been partially supported by Grant ECS8001763 of the National Science Foundation. 相似文献
5.
We consider the synthesis of linear control laws under one integral and several phase constraints on the basis of the Lyapunov function method and the technique of linear matrix inequalities. In particular, our method permits one to obtain suboptimal state or output feedbacks providing the minimum upper bound for a quadratic functional under phase and control constrains or the minimum bound for the maximum deviation of the controlled variable under one integral and several phase constraints. The synthesis is generalized to the case of nonstationary parametric perturbations in the plant. 相似文献
6.
Joachim Gwinner 《Optimization》2017,66(8):1323-1336
AbstractThis paper addresses a class of inequality constrained variational inequalities and nonsmooth unilateral variational problems. We present mixed formulations arising from Lagrange multipliers. First we treat in a reflexive Banach space setting the canonical case of a variational inequality that has as essential ingredients a bilinear form and a non-differentiable sublinear, hence convex functional and linear inequality constraints defined by a convex cone. We extend the famous Brezzi splitting theorem that originally covers saddle point problems with equality constraints, only, to these nonsmooth problems and obtain independent Lagrange multipliers in the subdifferential of the convex functional and in the ordering cone of the inequality constraints. For illustration of the theory we provide and investigate an example of a scalar nonsmooth boundary value problem that models frictional unilateral contact problems in linear elastostatics. Finally we discuss how this approach to mixed formulations can be further extended to variational problems with nonlinear operators and equilibrium problems, and moreover, to hemivariational inequalities. 相似文献
7.
G. V. Smirnov 《Journal of Optimization Theory and Applications》1996,88(3):671-688
We present necessary conditions of optimality for an infinitehorizon optimal control problem. The transversality condition is derived with the help of stability theory and is formulated in terms of the Lyapunov exponents of solutions to the adjoint equation. A problem without an exponential factor in the integral functional is considered. Necessary and sufficient conditions of optimality are proved for linear quadratic problems with conelike control constraints. 相似文献
8.
De Pinho M. D. R.; Vinter R. B.; Zheng H. 《IMA Journal of Mathematical Control and Information》2001,18(2):189-205
Necessary conditions in the form of maximum principles are derivedfor optimal control problems with mixed control and state constraints.Traditionally, necessary condtions for problems with mixed constraintshave been proved under hypothesis which include the requirementthat the Jacobian of the mixed constraint functional, with respectto the control variable, have full rank. We show that it canbe replaced by a weaker interiority hypothesis.This refinement broadens the scope of the optimality conditions,to cover some optimal control problems involving differentialalgebraic constraints, with index greater than unity. 相似文献
9.
We develop a search procedure for project scheduling problems with multiple resource constraints as well as precedence constraints. The procedure is applied to three popular search heuristics, simulated annealing, tabu search and genetic algorithms. In the heuristics, a solution is represented with a string of numbers each of which denotes priority of each activity. The priorities are used to select an activity for scheduling among competing ones. The search heuristics with this encoding method can always generate feasible neighbourhood solutions for a given solution. Moreover, this encoding method is very flexible in that problems with objective functions of a general functional form (such as a nonlinear function) and complex constraints can be considered without much difficulty. Results of computational tests on the performance of the search heuristics showed that the search heuristics, especially the simulated annealing and tabu search algorithms worked better than existing heuristics. 相似文献
10.
Tommaso Rigon 《商业与工业应用随机模型》2023,39(2):232-250
There is an increasingly rich literature about Bayesian nonparametric models for clustering functional observations. Most recent proposals rely on infinite-dimensional characterizations that might lead to overly complex cluster solutions. In addition, while prior knowledge about the functional shapes is typically available, its practical exploitation might be a difficult modeling task. Motivated by an application in e-commerce, we propose a novel enriched Dirichlet mixture model for functional data. Our proposal accommodates the incorporation of functional constraints while bounding the model complexity. We characterize the prior process through a urn scheme to clarify the underlying partition mechanism. These features lead to a very interpretable clustering method compared to available techniques. Moreover, we employ a variational Bayes approximation for tractable posterior inference to overcome computational bottlenecks. 相似文献
11.
We consider the asymptotics of the optimal value of the performance functional in an optimal control problem for a linear
system with rapid and slow variables, with convex terminal performance functional depending on the slow variables, and with
smooth geometric constraints on the control. We find sufficient conditions for the regularity of asymptotics and construct
an algorithm for finding the complete asymptotics of the optimal value of the performance functional. 相似文献
12.
In this paper, we investigate a constrained optimization problem with a quadratic cost functional and two quadratic equality constraints. It is assumed that the cost functional is positive definite and that the constraints are both feasible and regular (but otherwise they are unrestricted quadratic functions). Thus, the existence of a global constrained minimum is assured. We develop a necessary and sufficient condition that completely characterizes the global minimum cost. Such a condition is of essential importance in iterative numerical methods for solving the constrained minimization problem, because it readily distinguishes between local minima and global minima and thus provides a stopping criterion for the computation. The result is similar to one obtained previously by the authors. In the previous result, we gave a characterization of the global minimum of a constrained quadratic minimization problem in which the cost functional was an arbitrary quadratic functional (as opposed to positive-definite here) and the constraints were at least positive-semidefinite quadratic functions (as opposed to essentially unrestricted here). 相似文献
13.
Walter Alt Ursula Felgenhauer Martin Seydenschwanz 《Computational Optimization and Applications》2018,69(3):825-856
We investigate Euler discretization for a class of optimal control problems with a nonlinear cost functional of Mayer type, a nonlinear system equation with control appearing linearly and constraints defined by lower and upper bounds for the controls. Under the assumption that the cost functional satisfies a growth condition we prove for the discrete solutions Hölder type error estimates w.r.t. the mesh size of the discretization. If a stronger second-order optimality condition is satisfied the order of convergence can be improved. Numerical experiments confirm the theoretical findings. 相似文献
14.
We consider a singularly-perturbed nonconvex energy functional which arises in the study of microstructures in shape memory alloys. The scaling law for the minimal energy predicts a transition from a parameter regime in which uniform structures are favored, to a regime in which the formation of fine patterns is expected. We focus on the transition regime and derive the reduced model in the sense of \(\Gamma \)-convergence. The limit functional turns out to be similar to the Mumford–Shah functional with additional constraints on the jump set of admissible functions. One key ingredient in the proof is an approximation result for \(SBV^p\) functions whose jump sets have a prescribed orientation. 相似文献
15.
Lars Eldén 《BIT Numerical Mathematics》1990,30(3):466-483
We study a linear, discrete ill-posed problem, by which we mean a very ill-conditioned linear least squares problem. In particular we consider the case when one is primarily interested in computing a functional defined on the solution rather than the solution itself. In order to alleviate the ill-conditioning we require the norm of the solution to be smaller than a given constant. Thus we are lead to minimizing a linear functional subject to two quadratic constraints. We study existence and uniqueness for this problem and show that it is essentially equivalent to a least squares problem with a linear and a quadratic constraint, which is easier to handle computationally. Efficient algorithms are suggested for this problem. 相似文献
16.
Winnifried Wollner 《PAMM》2008,8(1):10873-10874
We are concerned with an interior penalty method for an optimal control problem with an elliptic PDE constraint and additional pointwise constraints on the gradient of the state variable. We will derive an estimator that gives qualitative information about the error in the cost functional due to the interior penalty parameter and for the discretization of the PDE. These can be used to balance the error contributions of both types of errors. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
17.
Thai Doan Chuong 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6312-6322
This paper is devoted to the study of the pseudo-Lipschitz property of the efficient (Pareto) solution map for the perturbed convex semi-infinite vector optimization problem (CSVO). We establish sufficient conditions for the pseudo-Lipschitz property of the efficient solution map of (CSVO) under continuous perturbations of the right-hand side of the constraints and functional perturbations of the objective function. Examples are given to illustrate the obtained results. 相似文献
18.
Monika Wolfmayr 《Numerical Methods for Partial Differential Equations》2017,33(2):403-424
In this work, new results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed, and fully computable lower bounds for the cost functional in addition to the already existing upper bounds. Using both, the lower and the upper bounds, we arrive at two‐sided estimates for the cost functional. We prove that these bounds finally lead to sharp, guaranteed and fully computable upper estimates for the discretization error in the state and the control of the optimal control problem. First numerical tests are presented confirming the efficiency of the a posteriori estimates derived. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 403–424, 2017 相似文献
19.
In this paper, a fast algorithm for Euler's elastica functional is proposed,
in which the Euler's elastica functional is reformulated as a constrained
minimization problem. Combining the augmented Lagrangian method and operator
splitting techniques, the resulting saddle-point problem is solved by a serial
of subproblems. To tackle the nonlinear constraints arising in the model, a novel
fixed-point-based approach is proposed so that all the subproblems either is a
linear problem or has a closed-form solution. We show the good performance of our
approach in terms of speed and reliability using numerous numerical examples on
synthetic, real-world and medical images for image denoising, image inpainting
and image zooming problems. 相似文献
20.
In this paper we characterize the upper semicontinuity of the feasible set mapping at a consistent linear semi-infinite system (LSIS, in brief). In our context, no standard hypothesis is required in relation to the set indexing the constraints and, consequently, the functional dependence between the linear constraints and their associated indices has no special property. We consider, as parameter space, the set of all LSIS having the same index set, endowed with an extended metric to measure the size of the perturbations. We introduce the concept of reinforced system associated with our nominal system. Then, the upper semicontinuity property of the feasible set mapping at the nominal system is characterized looking at the feasible sets of both systems. The fact that this characterization depends only on the nominal system, not involving systems in a neighbourhood, is remarkable. We also provide a necessary and sufficient condition for the aimed property exclusively in terms of the coefficients of the system. 相似文献