摘要:

A numerical method for unconstrained minization of nondifferentiable convex functions is proposed and studied. This method is based on a continuous approximations to the subdifferential. An algorithm for the construction of the continuous approximations is described. Results of numerical experiments are presented

ISSN:1055-6788    

DOI:10.1080/10556789808805683

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Exact penalty functions for nonsmooth constrained optimization problems are analyzed tfy using the notion of (Dini) Hadamard directional derivative with respect to the constraint set. Weak conditions are given guaranteeing equivalence of the sets of stationary, global minimum, local minimum points of the constrained problem and of the penalty function

ISSN:1055-6788    

DOI:10.1080/10556789808805684

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Primal-dual interior-point methods for linear programming are often motivated by a certaijn nonlinear transformation of the Karush-Kuhn-Tucker conditions of the logarithmic Barrier formulation. Recently, Nassar [5] studied the reciprocal Barrier function formulation of the problem. Using a similar nonlinear transformation, he proved local convergence fir Newton interior-point method on the resulting perturbed Karush-Kuhn-Tucker systerp. This result poses the question whether this method can exhibit fast convergence ral[e for linear programming. In this paper we prove that, for linear programming, Newton's method on the reciprocal Barrier formulation exhibits at best Q-linear convergence rattf. Moreover, an exact Q1factor is established which precludes fast linear convergence

ISSN:1055-6788    

DOI:10.1080/10556789808805685

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

A new and unified methodology for computing first order derivatives of functions obtained in complex multistep processes is developed on the basis of general expressions for differentiating a composite function. From these results, we derive the formulas for fap automatic differentiation of elementary functions, for gradients arising in optimal control problems, nonlinear programming and gradients arising in discretizations of processes governed by partial differential equations. In the proposed approach we start with a chosqn discretization scheme for the state equation and derive the exact gradient expression. Thus a unique discretization scheme is automatically generated for the adjoint equation For optimal control problems, the proposed computational formulas correspond to the integration of the adjoint system of equations that appears in Pontryagin's maximum principle. This technique appears to be very efficient, universal, and applicable to a wide variety of distributed controlled dynamic systems and to sensitivity analysis

ISSN:1055-6788    

DOI:10.1080/10556789808805686

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

A general approach to constructing iterative methods that solve variational inequaliti under mild assumptions is proposed. It is based on combining and modifying ide contained in various relaxation methods. The conditions under which the proposed metho attain linear convergence or terminate with a solution are also given

ISSN:1055-6788    

DOI:10.1080/10556789808805687

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

When nonsmooth, convex minimization problems are solved by subgradient optimization methods, the subgradients used will in generalnotaccumulate to subgradients which verify the optimality of a solution obtained in the limit. It is therefore not a straightforward task to monitor the progress of a subgradient method in terms of the approximate fulfillment of optimality conditions. Further, certain supplementary information, such as convergent estimates of Lagrange multipliers and convergent lower bounds on the optimal objective value, is not directly available in subgradient schemes

ISSN:1055-6788    

DOI:10.1080/10556789808805688

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

Interior point methods, especially the algorithms for linear programming problems are sensitive if there are unconstrained (free) variables in the problem. While replacing a free variable by two nonnegative ones may cause numerical instabilities, the implicit handling results in a semidefinite scaling matrix at each interior point iteration. In the paper we investigate the effects if the scaling matrix is regularized. Our analysis will prove that the effect of the regularization can be easily monitored and corrected if necessary. We describe the regularization scheme mainly for the efficient handling of free variables, but a similar analysis can be made for the case, when the small scaling factors are raised to larger values to improve the numerical stability of the systems that define the searcn direction. We will show the superiority of our approach over the variable replacement method on a set of test problems arising from water management application

ISSN:1055-6788    

DOI:10.1080/10556789808805689

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

In this paper we study the quality of semidefinite relaxation for a global quadratic optimization problem with diagonal quadratic consraints. We prove that such relaxation approximates the exact solution of the problem with relative accuracy μ = (π/2) – 1. We consider some applications of this result

ISSN:1055-6788    

DOI:10.1080/10556789808805690

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

ISSN:1055-6788    

DOI:10.1080/10556789808805691

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor

摘要:

We consider general, typically nonconvex, Quadratic programming Problem. The Semidefinite relaxation proposed by Shor provides bounds on the optimal solution, but it does not always provide sufficiently strong bounds if linear constraintare also involved. To get rid of the linear side-constraints, another, stronger convex relaxation is derved. This relaxation uses copositive matrices. Special cases are dicussed for which both relaxations are equal. At end of the paper, the complexity and solvablility of the relaxation are discussed.

ISSN:1055-6788    

DOI:10.1080/10556789808805692

出版商:Gordon and Breach Science Publishers    

年代:1998

数据来源: Taylor