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}
}
  • J. Borwein, A. Lewis
  • 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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