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Duality relationships for entropy-like minimization problems. (English) Zbl 0797.49030
The paper is concerned with the dual approach to the optimization problem \[ \inf\left\{ \int_ T \phi(x(t)) d\sigma(t)\mid x\in L^ p(T,[0, +\infty[, \sigma),\;Ax= b\right\}, \] where \(1\leq p\leq \infty\), \(b\in {\mathbf R}^ n\) and \(A: L^ p(T,[0,+ \infty[, \sigma)\to {\mathbf R}^ n\) is continuous. By using the authors [Math. Programming (to appear)] it is proved that a quasi-interior constraint qualification ensures that the primal and dual values are equal, with dual attainment. Additional conditions are given for the attainment of the primal value, and the direct computation of the primal optimal solution from the dual solution.
Reviewer: L.Ambrosio (Pisa)

MSC:
49N15 Duality theory (optimization)
90C25 Convex programming
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