In this paper we present an improved neural network to solve strictly convex quadratic programming(QP) problem. The proposed model is derived based on a piecewise equation correspond to optimality condition of convex (QP) problem and has a lower structure complexity respect to the other existing neural network model for solving such problems. In theoretical aspect, stability and global converge...

A methodology for safety verification using barrier certificates has been proposed recently. Conditions that must be satisfied by a barrier certificate can be formulated as a convex program, and the feasibility of the program implies system safety, in the sense that there is no trajectory starting from a given set of initial states that reaches a given unsafe region. The dual of this problem, i...

We introduce a new algorithm to check the local stability and compute the region of attraction of isolated equilibria of nonlinear systems with polynomial vector fields. First, we consider an arbitrary convex polytope that contains the equilibrium in its interior. Then, we decompose the polytope into several convex sub-polytopes with a common vertex at the equilibrium. Then, by using Handelman’...

economic dispatch with valve point effect and prohibited operating zones (pozs) is a non-convex and discontinuous optimization problem. harmony search (hs) is one of the recently presented meta-heuristic algorithms for solving optimization problems, which has different variants. the performances of these variants are severely affected by selection of different parameters of the algorithm. intel...

Let K be a convex subset of Rn containing a ball of finite radius centered at c0 and contained in a ball of finite radius R. We give an oracle-polynomial-time algorithm for the weak separation problem for K given an oracle for the weak optimization problem for K. This is done by reducing the weak separation problem for K to the convex feasibility (nonemptiness) problem for a set K ′, and then b...

This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of the iterates is ...

This paper addresses the problem of robust H2 and H∞ control of discrete linear time-invariant (LTI) systems with polytopic uncertainties via dynamic output feedback. The problem has been known to be difficult when a parameter dependent Lyapunov function is to be applied for a less conservative design due to non-convexity. Our approach is based on a novel bounding technique that converts the no...

A convex semidefinite programming problem is a convex constrained optimization problem, where the constraints are linear matrix inequalities, for which the standard Lagrangian condition is sufficient for optimality. However, this condition requires constraint qualifications to completely characterize optimality. We present a necessary and sufficient condition for optimality without a constraint...

In control related studies, convex liftings have been of use to solve inverse parametric linear/quadratic programming problem. This paper presents a so-called convex liftings based method for robust control design of constrained linear systems affected by bounded additive disturbances. It will be shown that a geometrical construction as convex lifting can be used in optimization-based control d...

When an inverse problem can be formulated so the data are minima of one of the variational problems of mathematical physics, feasibility constraints can be found for the nonlinear inversion problem. These constraints guarantee that optimal solutions of the inverse problem lie in the convex feasible region of the model space. Furthermore, points on the boundary of this convex region can be found...