摘要:

This paper investigates local convergence properties of the Lagrange-Newton method for optimization problems in reflexive Banach spaces. Sufficient conditions for quadratic convergence of optimal solutions and Lagrange multipliers are given. The results are applied to optimal control problems.

ISSN:0163-0563    

DOI:10.1080/01630569008816371

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We investigate here the simultaneous approximation of a functionfεCq[−1,1] by a polynomialPnfinterpolatingfand off(1),…f(q)by the respective derivatives ofPnf. The nodes for the interpolation consist ofn“basic” nodes in (−1,1) forn= 1,2,… augmented by“added” nodes for eachn, converging to −1 at the rateandother “added” nodes converging to 1 at the same rate. We show for instance that, ifqis even, in whichLnis the interpolation on the “basic” nodes. Similar results hold ifqis odd. No assumptions need be made about the nodes other than what is already stated. If, for example, one uses for eachnthe zero set of the Chebychev polynomial cos(narc cosx) as the basic nodes, then, and our results thus obtain the rate of convergence which is “best possible.” Similarly, the prescribed rate of convergence to +1 and −1 for the added nodes is the most minimal assumption which gives good approximation of derivatives. In particular, the added nodes can lie partially or completely on top of each other near or at ±1 for some of all values ofnor interspersed between the “basic” nodes with no ill effects.

ISSN:0163-0563    

DOI:10.1080/01630569008816372

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

A class of multiobjective fractional programming problems is considered and duality results are established in terms of properly efficient solutions of the primal and dual programs. Further a vector-valued ratio type Lagrangian is introduced and certain vector saddlepoint results are presented.

ISSN:0163-0563    

DOI:10.1080/01630569008816373

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

We consider best approximations in a real or complex normed linear space by elements of a finite dimensional subspace. It is the purpose of this paper to characterize, when a best approximation to a given element is strongly unique.

ISSN:0163-0563    

DOI:10.1080/01630569008816374

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Necessary conditions for optimal control problems with state-control variable inequality constraints are obtained via mathematical programming formulation and functional analysis in Banach space. These conditions are general ones that hold without any constraint qualifications but differentiability. Furthermore, these conditions are shown to be equivalent to the classical result in the presence of the linear independence constraint qualification.

ISSN:0163-0563    

DOI:10.1080/01630569008816375

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

A one parameter family of iterative methods for solving an operator equation with a bounded linear operator between Hilbert spaces is introduced and analyzed. The classical conjugate gradient method is included in the family as is a method due to Le Foll. The latter method is also studied without the assumption that the equation have a solution and convergence properties of the iterates are established in this setting. A general convergence theorem is given and a variety of known bounds for rates of convergence of the conjugate gradient method are extended to the entire class of methods.

ISSN:0163-0563    

DOI:10.1080/01630569008816376

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

In this paper an approximation theory is provided for the solutions of infinite dimensional Algebraic Riccati Equations, which in particular includes convergence of the approximating Riccati operators as well as convergence of the approximating gain operators. The main features which distinguish this paper from other work existing in the literature of Riccati approximation theory are: (i) the original free system only generates a strongly continuous semigroup; (ii) the input (control) operator is generally unbounded; and (iii) no “smoothing” hypothesis on the observation operator is assumed. The abstract theory is illustrated by several examples arising in boundary control problems for wave and plate equations.

ISSN:0163-0563    

DOI:10.1080/01630569008816377

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

A coupled elastic beam system with a controller at the hinged junction that has point-mass is formulated as an abstract evolution equation in the energy space. By the spectral analysis of the hybrid differential operators with mixed boundary-junction conditions, an alternative principle of stabilizability in terms of the beam lengths ρ1 and ρ2 is proved: (I) If ρ1/ρ2 equals a quotient of two positive roots (different or same) of the transcendental equation tanμ = tanhμ, then the pointwise stabilization of the system is impossible. (II) If ρ1/ρ2 does not equal any quotient described above, then the system is strongly stabilized in the energy space by a pointwise damping feedbackf(t) = −wt(ρ1,t) at the junction point x = ρ1. Furthermore in the first case it is proved that a combination of the above pointwise damping feedback and an appropriate quasi-pointwise damping feedback on one beam achieves the strong stabilization.

ISSN:0163-0563    

DOI:10.1080/01630569008816378

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

摘要:

Suppose the mapping T has more then one fixed point. If the iterationconverges, the limit will depend on the choice of the starting point. It is shown that for affine mappings this dependency can be described by solutions of certain linear equations.

ISSN:0163-0563    

DOI:10.1080/01630569008816379

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor

ISSN:0163-0563    

DOI:10.1080/01630569008816370

出版商:Marcel Dekker, Inc.    

年代:1990

数据来源: Taylor