Recently Tseng [Merit function for semidefinite complementarity, Mathematical Programming, 83, pp. 159-185, 1998] extended a class of merit functions, proposed by Z. Luo and P. Tseng [A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems: State of the Art, pp. 204-225, 1997], for the nonlinear complementarity problem (NCP) to the s...

This paper is devoted to consider the notions of complementary problem (CP) and set-valued complementary problem (SVCP). The set-valued complementary problem is compared with the classical single-valued complementary problem. Also, the solution set of the set-valued complementary problem is characterized. Our results illustrated by some examples. This paper is devoted to co...

This paper proposes a novel robust control scheme based on delay-dependent H∞for unified power quality conditioner (UPQC) in a microgrid under the influence of the delay and parameter uncertainties. A new UPQC model considering the effects of the delay and parameter uncertainties is established. Then, the H∞ controller is designed based on the cone complementarity linearization (CCL) algorithm....

Two results on the second-order-cone complementarity problem are presented. We show that the squared smoothing function is strongly semismooth. Under monotonicity and strict feasibility we provide a new proof, based on a penalized natural complementarity function, for the solution set of the second-order-cone complementarity problem being bounded. Numerical results of squared smoothing Newton a...

Finite automata (with outputs but no initial states) have been extensively used as models of computational complementarity, a property which mimics the physical complementarity. All this work was focussed on \frames", i.e., on xed, static, local descriptions of the system behaviour. In this paper we are mainly interested in the asymptotical description of complementarity. To this aim we will st...

Abstract: Our purpose of this paper is to solve a class of stochastic linear complementarity problems (SLCP) with finitely many elements. Based on a new stochastic linear complementarity problem function, a new semi-smooth least squares reformulation of the stochastic linear complementarity problem is introduced. For solving the semi-smooth least squares reformulation, we propose a feasible non...

The presence of complementarity constraints brings a combinatorial flavour to an optimization problem. A quadratic programming problem with complementarity constraints can be relaxed to give a semidefinite programming problem. The solution to this relaxation can be used to generate feasible solutions to the complementarity constraints. A quadratic programming problem is solved for each of these...

Computational complementarity was introduced to mimic the physical complementarity in terms of nite automata (with outputs but no initial state). Most of the work has been focussed on \frames", i.e., on xed, static, local descriptions of the system behaviour. The rst paper aiming to study the asymptotical description of complementarity was restricted to certain types of so c shifts. In this pap...

Projected dynamical systems have been introduced by Dupuis and Nagurney as dynamic extensions of variational inequalities. In the systems and control literature, complementarity systems have been studied as input/output dynamical systems whose inputs and outputs are connected through complementarity conditions. We show here that, under mild conditions, projected dynamical systems can be written...