# Duality relationships for entropy-like minimization problems

@article{Borwein1991DualityRF,
title={Duality relationships for entropy-like minimization problems},
author={Jonathan Michael Borwein and Adrian S. Lewis},
journal={Siam Journal on Control and Optimization},
year={1991},
volume={29},
pages={325-338}
}
• Published 1 February 1991
• Mathematics
• Siam Journal on Control and Optimization
This paper considers the minimization of a convex integral functional over the positive cone of an $L_p$ space, subject to a finite number of linear equality constraints. Such problems arise in spectral estimation, where the bjective 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…
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