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**Extra resources for Chiron: mechanising mathematics in OCAML**

**Sample text**

At ; 0/ ; t 2 T gg D M f0g C cone f. C / f1gg ; and h KR D cone .. 0n ; 0; 1/g : Obviously, PR is consistent if and only if F \ dom C ¤ ;. In particular, PR is consistent whenever C is bounded. The robust duality theory is a straightforward specification of the one exposed in Sect. 1, just defining the uncertainty set-valued mapping Un W T [ ft0Áo g Ã RnC1 , with t0 … T , such that Ut0 D . C / f1g f0g and Ut D at ; 0; b t for all t 2 T . Concerning the suitable numerical treatment of PR , it depends on its relevant properties: continuity of the constraint system, density assumption, boundedness of the optimal set SR , and boundedness and full dimensionality of FR .

A. A. 1007/978-1-4899-8044-1__3, © Miguel A. Goberna, Marco A. López 2014 39 40 3 Robust Linear Semi-infinite Optimization characteristic cone are denoted by cR , TR , FR ; SR , MR , and KR , respectively. The Haar dual problem of PR is denoted by DR . We also associate with P0 a robust dual problem (also called optimistic counterpart) D R such that the weak duality is always satisfied while the strong duality holds under mild conditions. We also examine the consistency of PR and its numerical tractability.

P /), whose desirable stability properties are the lower and upper semicontinuity. The optimal set and the feasible set mappings are set-valued mappings. The (primal) feasible set mapping F W ˘ Ã Rn associates with each 2 ˘ the feasible set F . / of P (the LSIO problem associated with ) while the (primal) optimal set mapping S W ˘ Ã Rn associates with each 2 ˘ the optimal set S . / of P . T / # D W ˘ ! T / set mapping S D W ˘ Ã RC assigning to 2 ˘ the optimal value, the feasible set and the optimal set of D, respectively.