Jerald P. Dauer

Positive proper efficient points and related cone results in Vector optimization theory

Positive proper efficient points are defined as solutions of appropriate linear scalar optimization problems. A geometric characterization of positive proper efficient points is given as well as conditions under which the set of positive proper efficient points is dense in the set of all efficient points. It is shown that these results are applicable in the normed vector lattices

Optimization over the efficient set

C[a,b]

Optimization over the efficient set using an active constraint approach

,

Constructing the set of efficient objective values in multiple objective linear programs

l^p

Exact Controllability of the Damped Wave Equation

, and

A combined constraint-space, objective-space approach for determining high-dimensional maximal efficient faces of multiple objective linear programs

L^p

Null Controllability of Semilinear Integrodifferential Systems in Banach Space

for

On degeneracy and collapsing in the construction of the set of objective values in a multiple objective linear program

1 leqq p leqq infty

On controllability of an elastic string with a viscous damping

, and that previous related results, which required the ordering cone to have a compact or weak-compact base, are not applicable in many normed vector lattices, including

Acoustic scattering by a narrow crack in an elastic plate

C[a,b]