Slide 10: two routes for nonconvex elements in disjuncts — (a) convexify disjuncts, then apply LOA (Ruiz-style); (b) Sawaya reformulation + global solver. Today GLOA (global NLP subproblems, MC++ affine cuts) is the only rigorous nonconvex route; there is no per-disjunct convexification feeding LOA.
Scope: per-disjunct convex relaxations (MC++ or alpha-BB-style, cf. C3) replacing nonconvex constraints in the discrete problem; LOA loop on the convexified GDP; optional refinement of the relaxations as the search narrows. Middle ground between LOA-as-heuristic and GLOA's expensive global subproblems; relates to Hooker's hull results for nonconvex disjuncts (notes on slide 6).
Part of roadmap epic #2 (item B8).
Slide 10: two routes for nonconvex elements in disjuncts — (a) convexify disjuncts, then apply LOA (Ruiz-style); (b) Sawaya reformulation + global solver. Today GLOA (global NLP subproblems, MC++ affine cuts) is the only rigorous nonconvex route; there is no per-disjunct convexification feeding LOA.
Scope: per-disjunct convex relaxations (MC++ or alpha-BB-style, cf. C3) replacing nonconvex constraints in the discrete problem; LOA loop on the convexified GDP; optional refinement of the relaxations as the search narrows. Middle ground between LOA-as-heuristic and GLOA's expensive global subproblems; relates to Hooker's hull results for nonconvex disjuncts (notes on slide 6).
Part of roadmap epic #2 (item B8).