This paper deals with Mixed Logical Dynamical (MLD) approach. It allows to model the hybrid systems involved continuous, discrete dynamics and constraints. The changes or the switches which may appear over such dynamics are modelled by using the auxiliary variables take into account the interconnections. The applicability of this approach is illustrated by the modelling of the two tank system. ...

A classic result by Cook, Gerards, Schrijver, and Tardos provides an upper bound of $$n \Delta $$ on the proximity optimal solutions Integer Linear Programming problem its standard linear relaxation. In this bound, n is number variables $$\Delta denotes maximum absolute values subdeterminants constraint matrix. Hochbaum Shanthikumar, Werman Magagnosc showed that same valid if a more general co...

Most industrial model predictive controllers (MPC) use the traditional two-layer structure developed in the early 1980’s, where the upper layer defines optimal steady-state targets for inputs and outputs, while the lower layer calculates the control moves that drive the system towards these steady-state targets. As a rule, both layers use continuous quadratic programming (QP) formulations to de...

Most industrial model predictive controllers (MPC) use the traditional two-layer structure developed in the early 1980’s, where the upper layer defines optimal steady-state targets for inputs and outputs, while the lower layer calculates the control moves that drive the system towards these steady-state targets. Typically both layers use continuous quadratic programming (QP) formulations to der...

Combinatorial optimization over continuous and integer variables was proposed recently as an useful tool for solving complex optimal control problems for linear hybrid dynamical systems formulated in discretetime. Current approaches are based on mixed-integer linear/quadratic programming (MIP), which provides the solution after solving a sequence of relaxed standard linear (or quadratic) progra...

This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and nonconvex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the liftand...

McGeoch and Wang (2013) recently obtained optimal or near-optimal solutions to some quadratic unconstrained boolean optimization (QUBO) problem instances using a 439 qubit D-Wave Two quantum computing system in much less time than with the IBM ILOG CPLEXmixed-integer quadratic programming (MIQP) solver. The problems studied by McGeoch and Wang are defined on subgraphs – with up to 439 nodes – o...

This paper addresses the problem of generating strong convex relaxations of Mixed Integer Quadratically Constrained Programming (MIQCP) problems. MIQCP problems are very difficult because they combine two kinds of non-convexities: integer variables and non-convex quadratic constraints. To produce strong relaxations of MIQCP problems, we use techniques from disjunctive programming and the lift-a...

We present a new tree-search algorithm for solving mixed-integer nonlinear programs (MINLPs). Rather than relying on computationally expensive nonlinear solves at every node of the branchand-bound tree, our algorithm solves a quadratic approximation at every node. We show that the resulting algorithm retains global convergence properties for convex MINLPs, and we present numerical results on a ...

JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax. JuMP takes advantage of advanced features of the Julia programming language to offer unique functionality while achieving performance on par with commercial modeling tools f...