Symmetric dual multiobjective programming

In this paper a pair of symmetric dual multiobjective programming problems is formulated and the duality theorems are established for pseudo-convex/pseudo-concave functions.     

Symmetric dual fractional programming

A pair of symmetric dual fractional programming problems is formulated and appropriate duality theorems are established.

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Zusammenfassung Es wird ein symmetrisches Paar primaler und dualer Quotientenprogramme eingeführt, für das Dualitätsbeziehungen hergeleitet werden.

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Research by this author was carried out while he was a visiting research fellow at the University of Melbourne.     

Real perturbation values and real quadratic forms in a complex vector space

A sequence of real numbers connected to a complex matrix is introduced. It is shown how these real perturbation values can be computed and that they have several properties similar to the singular values. The so-called real pseudospectra and real stability radii can be computed using the real perturbation values. The main result concerns the signature of real quadratic forms in complex vector spaces.     

The generalized Hodge conjecture for the quadratic complex of lines in projective four–space

We verify the generalized Hodge conjecture GHC(X,5,2) for the quadratic complex of lines in projective four–space. Received: 27 February 1998 / Revised version: 13 May 1998     

Convex dual for quadratic concave fractional programs

For a fractional program with a quadratic numerator and an arbitrary concave denominator, a new convex dual program is derived. Concepts of conjugate duality are used to obtain an explicit representation of the dual.The authors are grateful to two anonymous referees and the Associate Editor for their comments.     

Classification of self dual quadratic bent functions

We classify all self dual and anti self dual quadratic bent functions in 2n variables under the action of the orthogonal group O(2n,\mathbb F₂){{O}(2n,\mathbb F_2)} . This is done through a classification of all 2n × 2n involutory alternating matrices over \mathbb F₂{\mathbb F_2} under the action of the orthogonal group. The sizes of the O(2n,\mathbb F₂){{O}(2n,\mathbb F_2)} -orbits of self dual and anti self dual quadratic bent functions are determined explicitly.     

Symmetric low‐rank corrections to quadratic models

In this paper, we study the quadratic model updating problems by using symmetric low‐rank correcting, which incorporates the measured model data into the analytical quadratic model to produce an adjusted model that matches the experimental model data, and minimizes the distance between the analytical and updated models. We give a necessary and sufficient condition on the existence of solutions to the symmetric low‐rank correcting problems under some mild conditions, and propose two algorithms for finding approximate solutions to the corresponding optimization problems. The good performance of the two algorithms is illustrated by numerical examples. Copyright © 2008 John Wiley & Sons, Ltd.     

A DUAL NON-LINEAR PROGRAM

In the paper a dual of a nonlinear fractional functional programming problem has beenformulated.This problem can be used to obtain a solution of the mixed 0—1 integer linearprogramming problem.Some properties related to the primal and dual have been given.     

Properties of quadratic maps in a Banach space

Translated from Matematicheskie Zametki, Vol. 50, No. 4, pp. 10–20, October, 1991.     

Infinite positive-definite quadratic programming in a Hilbert space

This note generalizes the results of Benson, Smith, Schochetman, and Bean (Ref. 1) regarding the minimization of a positive-definite functional over the countable intersection of closed convex sets in a Hilbert space. A finite approximating subproblem for the general case is shown to have the same strong convergence properties of the earlier work without any of the specialized structures imposed therein. In particular, the current development does not rely on any properties ofl ² and does not require the Hilbert space to be separable.     

On quadratic APN functions and dimensional dual hyperovals

In this paper we characterize the d-dimensional dual hyperovals in PG(2d + 1, 2) that can be obtained by Yoshiara’s construction (Innov Incid Geom 8:147–169, 2008) from quadratic APN functions and state a one-to-one correspondence between the extended affine equivalence classes of quadratic APN functions and the isomorphism classes of these dual hyperovals.     

The moduli space of quadratic rational maps

Let be the space of quadratic rational maps , modulo the action by conjugation of the group of Möbius transformations. In this paper a compactification of is defined, as a modification of Milnor's , by choosing representatives of a conjugacy class such that the measure of maximal entropy of has conformal barycenter at the origin in and taking the closure in the space of probability measures. It is shown that is the smallest compactification of such that all iterate maps extend continuously to , where is the natural compactification of coming from geometric invariant theory.