We present a proactive energy management framework that integrates predictive dynamic building models and day-ahead forecasts of disturbances affecting efficiency and costs. This enables an efficient management of resources and an accurate prediction of the daily electricity demand profile. The strategy is based on the on-line solution of mixed-integer nonlinear programming problems. The framework is … Read more
We present a mixed-integer nonlinear programming (MINLP) formulation to achieve minimum-cost designs for reinforced concrete (RC) structures that satisfy building code requirements. The objective function includes material and labor costs for concrete, steel reinforcing bars, and formwork according to typical contractor methods. Restrictions enforce correct geometry of the cross-section dimensions for each element and relative … Read more
We call ”on/off” constraint an algebraic constraint that is activated if and only if a corresponding boolean variable is turned ”on” or equal to 1. Our main subject of interest is to derive tight convex formulations of Mixed Integer NonLinear Programs (MINLPs) featuring ”on/off” constraints. We study the simple set defined by one ”on/off” constraint … Read more
This paper provides a survey of recent progress and software for solving mixed integer nonlinear programs (MINLP) wherein the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables. Convex MINLPs have received sustained attention in very years. By exploiting analogies to the case of … Read more
We consider two-stage quadratic integer programs with stochastic right-hand sides, and present an equivalent reformulation using value functions. We fi rst derive some basic properties of value functions of quadratic integer programs. We then propose a two-phase solution approach. The first phase constructs the value functions of quadratic integer programs in both stages. The second phase … Read more
In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems arise, e.g., from the outer convexification of integer control decisions. We treat this optimal control problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved … Read more
In this paper we survey recent work on the perspective reformulation approach that generates tight, tractable relaxations for convex mixed integer nonlinear programs (MINLP)s. This preprocessing technique is applicable to cases where the MINLP contains binary indicator variables that force continuous decision variables to take the value 0, or to belong to a convex set. … Read more
Automatic verification of computer code is of paramount importance in embedded systems supplying essential services. One of the most important verification techniques is static code analysis by abstract interpretation: the concrete semantics of a programming language (i.e.the values $\chi$ that variable symbols {\tt x} appearing in a program can take during its execution) are replaced … Read more
In an important paper, Burer recently showed how to reformulate general mixed-binary quadratic optimization problems (QPs) into copositive programs where a linear functional is minimized over a linearly constrained subset of the cone of completely positive matrices. In this note we interpret the implication from a topological point of view, showing that the Minkowski sum … Read more
Mixed Integer Nonlinear Programming (MINLP) problems present two main challenges: the integrality of a subset of variables and nonconvex (nonlinear) objective function and constraints. Many exact solvers for MINLP are branch-and-bound algorithms that compute a lower bound on the optimal solution using a linear programming relaxation of the original problem. In order to solve these … Read more