Multipliers of classes of cauchy transforms

The analytic map g on the unit disk D is said to induce a multiplication operator L from the Banach space X to the Banach space Y if L(f)=f·g∈Y for all f∈X. For z ∈ D and α>0 the families of weighted Cauchy transforms F_α are defined by ?(z) = ∫_T K_x ^α (z)dμ(x) where μ(x) is complex Borel measures, x belongs to the unit circle T and the kernel K_x (z) = (1- xz)^?1. In this article we will explore the relationship between the compactness of the multiplication operator L acting on F ₁ and the complex Borel measures μ(x). We also give an estimate for the essential norm of L     

On the continuity of a Lagrangian multiplier function in input optimization

We show that a Lagrangian multiplier function in input optimization is generally discontinuous on regions of stability and then we find conditions for its continuity.Research partly supported by the Natural Sciences and Engineering Research Council of Canada.Presented at TIMS/ORSA Meeting in Boston, Massachusetts, April 29-May 1, 1985.The contribution of this author is part of his M.Sc. thesis in Applied Mathematics at McGill University.     

A convergence proof for linear mean value cross decomposition

The mean value cross decomposition method for linear programming problems is a modification of ordinary cross decomposition that eliminates the need for using the Benders or Dantzig-Wolfe master problem. It is a generalization of the Brown-Robinson method for a finite matrix game and can also be considered as a generalization of the Kornai-Liptak method. It is based on the subproblem phase in cross decomposition, where we iterate between the dual subproblem and the primal subproblem. As input to the dual subproblem we use the average of a part of all dual solutions of the primal subproblem, and as input to the primal subproblem we use the average of a part of all primal solutions of the dual subproblem. In this paper we give a new proof of convergence for this procedure. Previously convergence has only been shown for the application to a special separable case (which covers the Kornai-Liptak method), by showing equivalence to the Brown-Robinson method.     

Generalized Hörmander's conditions, commutators and weights

We present a general framework to deal with commutators of singular integral operators with BMO functions. Hörmander type conditions associated with Young functions are assumed on the kernels. Coifman type estimates, weighted norm inequalities and two-weight estimates are considered. We give applications to homogeneous singular integrals, Fourier multipliers and one-sided operators.     

1.5-Q-superlinear convergence of an exterior-point method for constrained optimization

We introduce and analyze an exterior-point method (EPM) for constrained optimization problems with both inequality constraints and equations. We show that under the standard second-order optimality conditions the EPM converges to the primal–dual solution with 1.5-Q-superlinear rate. Dedicated to Professor Gil Strang on the occasion on his 70th birthday.     

A re-scaled twin augmented Lagrangian algorithm for saddle point seeking

In [A. Ouorou, A primal-dual algorithm for monotropic programming and its application to network optimization, Computational Optimization and Application 15 (2002) 125–143], a block-wise Gauss–Seidel method has been developed for monotropic programming problems, using two different quadratic augmented Lagrangian functions defined for the primal and the dual problems. In this paper, we extend the concept by introducing a nonlinear re-scaling principle obtained recently by Polyak [R. Polyak, Nonlinear rescaling vs smoothing technique in constrained optimization, Mathematical Programming 92 (2002) 197–235].     

Fredholmness of multipliers on Hardy–Sobolev spaces

This paper discusses the Fredholmness of multipliers on Hardy–Sobolev Spaces and obtains an index formula for the multipliers with some special symbols. Our results show that Hardy–Sobolev spaces have richer properties than classical holomorphic function spaces, and the behavior of the operators on these spaces is complex. Some methods of Hardy or Bergman spaces fail in the case of the Hardy–Sobolev space.     

First and second order sensitivity analysis of nonlinear programs under directional constraint qualification conditions

An extension and unification is presented, of the recent results of Shapiro [16] and Gatjvin & Janin [8] about second order differentiability of the optimal value function and directional differentiability of optimal solutions of perturbed mathematical programs, under a relaxed directional version of the Managasarian-Fromowitz constraint qualification condition introduced by Gollan [9]     

Multipliers spaces, Muckenhoupt weights and pseudo-differential operators

Let σ(x,ξ) be a sufficiently regular function defined on Rd×Rd. The pseudo-differential operator with symbol σ is defined on the Schwartz class by the formula

     

Convolutions,Tensor Products and Multipliers of the Orlicz-Lorentz Spaces

In this paper, the authors first give the properties of the convolutions of OrliczLorentz spaces Λ1,wand Λ2,won the locally compact abelian group. Secondly, the authors obtain the concrete representation as function spaces for the tensor products of Orlicz-Lorentz spaces Λ1,wand Λ2,w, and get the space of multipliers from the spaceΛ1,wto the space M2*,w. Finally, the authors discuss the homogeneous properties for the Orlicz-Lorentz space Λp,q,w.