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The Perspective Relaxation (PR) is a general approach for constructing tight approximations to MixedInteger NonLinear Problems with semicontinuous variables. The PR of a MINLP can be formulated either as a Mixed-Integer Second-Order Cone Program (provided that the original objective function is SOCPrepresentable), or as a Semi-Infinite MINLP. In this paper, we show that under some further assumptions (rather restrictive, but satisfied in several practical applications), the PR of Mixed-Integer Quadratic Program can also be reformulated as a piecewise linear-quadratic problem, ultimately yielding a QP relaxation of roughly the same size of the standard continuous relaxation. Furthermore, if the original problem has some exploitable structure, then this structure is typically preserved in the reformulation, thus allowing to construct specialized approaches for solving the PR. We report on implementing these ideas on two MIQPs with appropriate structure: a sensor placement problem and a Quadratic-cost (single-commodity) network design problem.

Italy was a country severely hit by the first coronavirus disease 2019 (COVID-19) pandemic wave in early 2020. Mortality studies have focused on the overall excess mortality observed during the pandemic. This paper investigates the cause-specific mortality in Italy from March 2020 to April 2020 and the variation in mortality rates compared with those in 2015–2019 regarding sex, age, and epidemic area. Causes of death were derived from the national cause-of-death register. COVID-19 was the leading cause of death among males and the second leading cause among females. Chronic diseases, such as diabetes and hypertensive, ischemic heart, and cerebrovascular diseases, with decreasing or stable mortality rates in 2015–2019, showed a reversal in the mortality trend. Moreover, mortality due to pneumonia and influenza increased. No increase in neoplasm mortality was observed. Among external causes of death, mortality increased for accidental falls but reduced for transport accidents and suicide. Mortality from causes other than COVID-19 increased similarly in both genders and more at ages 65 years or above. Compared with other areas in Italy, the Lombardy region showed the largest excess in mortality for all leading causes. Underdiagnosis of COVID-19 at the beginning of the pandemic may, to some extent, explain the mortality increase for some causes of death, especially pneumonia and other respiratory diseases.