Extended Formulations in Mixed-integer Convex Programming

We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.Comment: To be presented at IPCO 201

Actinomyces associated with persistent vaginal granulation tissue.

BACKGROUND: We report a case of symptomatic actinomycosis associated with vaginal suture erosion and granulation tissue refractory to conservative management, in an outpatient setting. CASE: Three months after total vaginal hysterectomy and uterosacral ligament vaginal vault suspension, a woman complained of painless, intermittent vaginal discharge and spotting. Despite cauterization of granulation tissue, vaginal spotting persisted for another month. On re-examination, braided polyester suture that was found underlying the granulation tissue was removed. Recurrent symptoms, together with a biopsy revealing actinomycetes, prompted a trial of oral penicillin VK. With persistent symptoms and discomfort during attempts in the outpatient clinic, the woman eventually required suture removal in the operating room. Her symptoms subsequently resolved without recurrence, and no further antibiotic treatment was required. CONCLUSIONS: Actinomyces may be associated with persistent granulation tissue and vault suspension suture material. In rare circumstances, when tissue debridement and suture removal in the clinic is unsatisfactory, surgical intervention in the operating room may be necessary. Ten days of antibiotic therapy alone did not eradicate the granulation tissue, and symptoms resolved only after complete removal of the underlying permanent suture