What is it about?
This paper has appeared in the book CHARLEMAGNE AND HIS HERITAGE 1200 YEARS OF CIVILIZATION AND SCIENCE IN EUROPE that has celebrated the tradition of scientific work located in Aachen. The topic is the study of the optimal value function of a parametric optimization problem when the parameter approaches a singular parameter where the Slater condition is violated.
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Why is it important?
The Slater condition is a well known sufficient condition for stability of the ouput of a parametric optimization problem. What happens in the limit cases where the Slater condition is violated? This is the case for example if for box constraints the lower bound and the upper bound come closer and closer until they are identical. This process does not necessarily lead to a singularity in the optimal value function. In the paper, a sufficient conditions for a transition with a differentiable optimal value function is presented.
Read the Original
This page is a summary of: Parametric Convex Optimization: One-Sided Derivatives of the Value Function in Singular Parameters, January 1998, Brepols Publishers NV,
DOI: 10.1484/m.sths-eb.4.2017057.
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