In this paper, a trust region method for generalized semi-infinite programming problems is presented. The method is based on [O. Yi-gui, “A filter trust region method for solving semi-infinite programming problems”, J. Appl. Math. Comput. 29, 311 (2009)]. We transformed the method from standard to generalized semi-infinite programming problems. The semismooth reformulation of the Karush–Kuhn–Tu...

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...

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...

Given an edge-weighted graph and an integer k, the generalized graph coloring problem is the problem of partitioning the vertex set into k subsets so as to minimize the total weight of the edges that are included in a single subset. We recall a result on the equivalence between Karush–Kuhn–Tucker points for a quadratic programming formulation and local optima for the simple 5ip-neighborhood. We...

The paper presents concrete realizations of quasi-Newton methods for solving several standard problems including complementarity problems, special variational inequality problems, and the Karush–Kuhn–Tucker (KKT) system of nonlinear programming. A new approximation idea is introduced in this paper. The Q-superlinear convergence of the Newton method and the quasiNewton method are established und...

We analyze the perturbations of quasi-solutions to a parameterized nonlinear programming problem, these being feasible solutions accompanied by a Lagrange multiplier vector such that the Karush-Kuhn-Tucker optimality conditions are satisfied. We show under a standard constraint qualification, not requiring uniqueness of the multipliers, that the quasi-solution mapping is differentiable in a gen...

A finite-time attitude compensation control scheme is developed for an over-activated rigid spacecraft subject to actuator faults, misalignment, external disturbances and uncertain inertia parameters. The controller is synthesised based on the sliding mode control theory, and guarantees the finite-time reachability of the system states. A sufficient condition for the controller to accommodate m...

This letter investigates the resource allocation problem in device-to-device (D2D) communications underlaying a non-orthogonal multiple access (NOMA)-based cellular network, where both cellular users and D2D users harvest energy from the hybrid access point in the downlink and transmit information in the uplink. We propose a low-complexity iterative algorithm to maximize the energy efficiency o...

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...

In constrained nonlinear optimization, the squared slack variables can be used to transform a problem with inequality constraints into a problem containing only equality constraints. This reformulation is usually not considered in the modern literature, mainly because of possible numerical instabilities. However, this argument only concerns the development of algorithms, and nothing stops us in...