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Duality Relationships for Entropy-Like Minimization Problems
Abstract
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 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.
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Cited by
Disciplined Convex Programming
Grant, M., Boyd, S., & Ye, Y. (2006) · Nonconvex Optimization and Its Applications · doi:10.1007/0-387-30528-9_7 · Cited by 1,026
Scaling algorithms for unbalanced optimal transport problems
Chizat, L., Peyré, G., Schmitzer, B., & Vialard, F.-X. (2018) · Mathematics of Computation · doi:10.1090/mcom/3303 · Cited by 336
Metadata
- Authors
- Borwein, J. M., & Lewis, A. S.
- Venue
- SIAM Journal on Control and Optimization
- Published
- 1991-03
- Volume
- 29
- Issue
- 2
- Pages
- 325-338
- ISSN
- 0363-0129 (ISSN-L)
- 1095-7138
- OpenAlex
- W2096876265
- Cited by
- 211
- References
- 0
- FWCI
- 6.62
- Type
- journal article
- Language
- en
- Open access
- closed
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- Borwein, J. M., & Lewis, A. S. (1991). Duality Relationships for Entropy-Like Minimization Problems. SIAM Journal on Control and Optimization. https://doi.org/10.1137/0329017
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