We propose a new algorithm for the nonlinear inequality constrained minimization problem, and prove that it generates a sequence converging to points satisfying the KKT second order necessary conditions for optimality. The algorithm is a line search algorithm using directions of negative curvature and it can be viewed as a non trivial extension of corresponding known techniques from unconstrain...

In this paper a family of trust{region interior{point SQP algorithms for the solution of a class of minimization problems with nonlinear equality constraints and simple bounds on some of the variables is described and analyzed. Such nonlinear programs arise e.g. from the discretization of optimal control problems. The algorithms treat states and controls as independent variables. They are desig...

1 The " convex " KKT theorem: a recapitulation We recall the Karush-Kuhn-Tucker theorem for convex programming, as treated in the previous lecture (see Corollary 3.5 of [OSC]).

Abstract A new fast and efficient algorithm for the solution of the dynamic optimization problem resulted from the implementation of a model predictive control (MPC) framework in highly nonlinear dynamic systems is presented. The sequence of the optimal control actions is obtained through the solution of the parameterized set of the Karush-KuhnTucker (KKT) optimality conditions for the nonlinea...

Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Th...

We consider the stability of the feedback connection of a linear time invariant (LTI) plant with a static nonlinearity expressed by a certain class of quadratic program. By generalizing the class of candidate Lyapunov functions we improve on existing results in the literature. A Lyapunov function is constructed via the S-procedure from quadratic constraints established using the Karush-Kuhn-Tuc...

This paper shows how to construct and implement explicit MPC feedback laws for systems with a large number of states. Specifically, the construction of critical regions of the explicit MPC solution is replaced by a two-step procedure. First, all optimal active sets are enumerated off-line and corresponding KKT matrices are pre-factored. Then, in the on-line step, the optimal control inputs are ...

This article illustrates the general problem known as ‘simulation optimization’ through an (s,S) inventory management system. In this system, the goal function to be minimized is the expected value of specific inventory costs. Moreover, specific constraints must be satisfied for some random simulation responses, namely the service or fill rate, and for some deterministic simulation inputs, name...

We consider the speed scaling problem of scheduling a collection of tasks with release times, deadlines, and sizes so as to minimize the energy recharge rate. This is the first theoretical investigation of speed scaling for devices with a regenerative energy source. We show that the problem can be expressed as a polynomial sized convex program. We show that using the KKT conditions, one can obt...