The aim of solving the Optimal Power Flow problem is to determine the optimal state of an electric power transmission system, that is, the voltage magnitude and phase angles and the tap ratios of the transformers that optimize the performance of a given system, while satisfying its physical and...

We demonstrate a real-world application of the interactive multiple objective optimization (MOO) approach to the simultaneous setting of input and output amounts for the opening of new branches. As illustrated by the case example, all the branches of a fast-food company employ multiple inputs to...

In Bertuzzi et al. [1] we addressed the problem of finding the optimal radiotherapy fractionation scheme, representing the response to radiation of tumour and normal tissues by the LQ model including exponential repopulation and sublethal damage due to incomplete repair. We formulated the...

We consider low-rank semidefinite programming (LRSDP) relaxations of ±1 quadratic problems that can be formulated as the nonconvex nonlinear programming problem of minimizing a quadratic function subject to separable quadratic equality constraints. We prove the equivalence of the LRSDP problem...

Agricultural water trade has been adopted in many countries as a measure to overcome water deficiency facing irrigated regions. When correctly applied, the system can allocate more water to more productive farmers, thereby improving efficiency in resource utilisation. Despite this enormous...

Monetary Unit Sampling (MUS), also known as Dollar-Unit Sampling, is a popular sampling strategy in Auditing, in which all units are to be randomly selected with probabilities proportional to the book value. However, if units sizes have very large variability, no vector of probabilities exists...

Carbon emission reduction is a long-term strategy for China to promote its economic and social development. However, emission reduction often involves a huge amount of technological investment, which could vary substantially across different provinces due to their discrepancy in economic and...

We report the analytical study of a constrained optimization problem which consists in finding the minimal value of the largest entry of a vector d in R5, with constraints involving the entries sum and the squared entries sum. The solution of the problem studied in this paper provides the proof...

In this note we give an elementary proof of the Fritz-John and Karush-Kuhn-Tucker conditions for nonlinear finite dimensional programming problems with equality and/or inequality constraints.The proof avoids the implicit function theorem usually applied when dealing with equality constraints and...