https://ogma.newcastle.edu.au/vital/access/ /manager/Index ${session.getAttribute("locale")} 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13008 Wed 11 Apr 2018 16:41:49 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:2667 Wed 11 Apr 2018 16:03:13 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13031 p space, subject to a finite number of linear equality constraints. Such problems arise in spectralestimation, where the objective function is often entropy-like, and in constrained approximation. The Lagrangian dual problem is finite-dimensional and unconstrained. Under a quasi-interior constraint qualification, the primal and dual values are equal, with dual attainment. Examples show the primal value may not be attained. Conditions are given that ensure that the primal optimal solution can be calculated directly from a dual optimum. These conditions are satisfied in many examples.]]> Wed 11 Apr 2018 14:04:12 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:13096 p spectral estimation problem. The authors use a new constraint qualification (BWCQ) for infinite-dimensional convex programs with linear type constraints recently introduced in [Borwein and Wolkowicz, Math. Programming, 35 (1986), pp. 83-96]. This allows direct derivation of the explicit optimal solution of the problem as presented in [Goodrich and Steinhardt, SIAM J. Appl. Math., 46 (1986), pp. 417-426], and establishment of the existence of a simple and computationally tractable unconstrained Lagrangian dual problem. Moreover, the results illustrate that (BWCQ) is more appropriate to spectral estimation problems than the traditional Slater condition (which may only be applied after transformation of the problem into an L_p space [Goodrich and Steinhardt, op. cit.] and which therefore yields only necessary conditions).]]> Tue 28 May 2019 16:25:49 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:14073 1 approximation, constrained approximation and interpolation, spectral estimation, semi-infinite transportation problems and the generalized market area problem of Lowe and Hurter (1976). As in Part I, we shall use lattice notation extensively, but, as we illustrated there, in concrete examples lattice-theoretic ideas can be avoided, if preferred, by direct calculation.]]> Sat 24 Mar 2018 08:22:32 AEDT ]]>