The goal of multi-parametric quadratic programming (mpQP) is to compute analytic solutions to parameter-dependent constrained optimization problems, e.g., in the context of explicit linear MPC. We propose an improved combinatorial mpQP algorithm that is based on implicit enumeration of all possible optimal active sets and a simple saturation matrix pruning criterion which uses geometric propert...

In 1] a branch-and-bound implicit enumeration algorithm is described whose purpose is to generate a feasible schedule, if any, for each processor on a multiprocessing node running hard real-time processes. The optimization criterion is to minimize process lateness deened as the diierence between the process completion time and deadline. We show in this correspondence that this algorithm does no...

The Continuous Dynamic Network Loading problem is here addressed for given splitting rates, hence allowing for implicit path enumeration. To this aim, a macroscopic flow model for road links based on the Kinematic Wave Theory is coupled with a node model with priority rules at intersections, thus reproducing congested networks including queue spillback. The result is the General Link Transmissi...

S. M. Robinson published in 1980 a powerful theorem about solutions to certain “generalized equations” corresponding to parameterized variational inequalities which could represent the first-order optimality conditions in nonlinear programming, in particular. In fact, his result covered much of the classical implicit function theorem, if not quite all, but went far beyond that in ideas and form...

Current methods for building models using implicit volume techniques present problems defining accurate and controllable blend shapes between implicit primitives. We present new methods to extend the freedom and controllability of implicit volume modeling. The main idea is to use a free-form curve to define the profile of the blend region between implicit primitives. The use of a free-form impl...

In this paper, we study the existence of solutions to boundary value problem for implicit differential equations involving generalized fractional derivative via fixed point methods.

LOW-RANK ITERATIVE METHODS FOR PROJECTED GENERALIZED LYAPUNOV EQUATIONS TATJANA STYKEL Abstract. We generalize an alternating direction implicit method and the Smith method for large-scale projected generalized Lyapunov equations. Such equations arise in model reduction of descriptor systems. Low-rank versions of these methods are also presented, which can be used to compute low-rank approximat...

In this paper, we introduce the system of generalized vector equilibrium problems which includes as special cases the system of generalized implicit vector variational inequality problems, the system of generalized vector variational and variational-like inequality problems and the system of vector equilibrium problems. By using a maximal element theorem, we establish existence results for a so...