Reducing the projection onto the monotone extended second-order cone to the pool-adjacent-violators algorithm of isotonic regression. (English) Zbl 1531.90130
Summary: This paper introduces the monotone extended second-order cone (MESOC), which is related to the monotone cone and the second-order cone. Some properties of the MESOC are presented and its dual cone is computed. Projecting onto the MESOC is reduced to the pool-adjacent-violators algorithm (PAVA) of isotonic regression. An application of MESOC to portfolio optimization is provided. Some broad descriptions of possible MESOC-regression models are also outlined.
MSC:
| 90C33 | Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) |
| 26B35 | Special properties of functions of several variables, Hölder conditions, etc. |
| 49K45 | Optimality conditions for problems involving randomness |
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