A new use of Douglas–Rachford splitting for identifying infeasible, unbounded, and pathological conic programs
| Autor: | Wotao Yin, Yanli Liu, Ernest K. Ryu |
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| Rok vydání: | 2018 |
| Předmět: |
Mathematical optimization
021103 operations research General Mathematics Numerical analysis Subroutine 0211 other engineering and technologies 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Identification (information) Hyperplane Iterated function Conic section Simple (abstract algebra) 0101 mathematics Software Mathematics |
| Zdroj: | Mathematical Programming. 177:225-253 |
| ISSN: | 1436-4646 0025-5610 |
| DOI: | 10.1007/s10107-018-1265-5 |
| Popis: | In this paper, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglas–Rachford splitting. When an optimization program is infeasible, unbounded, or pathological, the iterates of Douglas–Rachford splitting diverge. Somewhat surprisingly, such divergent iterates still provide useful information, which our method uses for identification. In addition, for strongly infeasible problems the method produces a separating hyperplane and informs the user on how to minimally modify the given problem to achieve strong feasibility. As a first-order method, the proposed algorithm relies on simple subroutines, and therefore is simple to implement and has low per-iteration cost. |
| Databáze: | OpenAIRE |
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