Imputing a variational inequality function or a convex objective function: A robust approach
| Autor: | Alexandre M. Bayen, Jerome Thai |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Convex analysis
Mathematical optimization 021103 operations research Karush–Kuhn–Tucker conditions Duality gap Applied Mathematics 0211 other engineering and technologies Linear matrix inequality Duality (optimization) 020206 networking & telecommunications 02 engineering and technology Nonlinear programming Variational inequality Convex optimization 0202 electrical engineering electronic engineering information engineering Analysis Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 457:1675-1695 |
| ISSN: | 0022-247X |
| Popis: | To impute the function of a variational inequality and the objective of a convex optimization problem from observations of (nearly) optimal decisions, previous approaches constructed inverse programming methods based on solving a convex optimization problem [17] , [7] . However, we show that, in addition to requiring complete observations, these approaches are not robust to measurement errors, while in many applications, the outputs of decision processes are noisy and only partially observable from, e.g., limitations in the sensing infrastructure. To deal with noisy and missing data, we formulate our inverse problem as the minimization of a weighted sum of two objectives: 1) a duality gap or Karush–Kuhn–Tucker (KKT) residual, and 2) a distance from the observations robust to measurement errors. In addition, we show that our method encompasses previous ones by generating a sequence of Pareto optimal points (with respect to the two objectives) converging to an optimal solution of previous formulations. To compare duality gaps and KKT residuals, we also derive new sub-optimality results defined by KKT residuals. Finally, an implementation framework is proposed with applications to delay function inference on the road network of Los Angeles, and consumer utility estimation in oligopolies. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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