A canonical duality approach for the solution of affine quasi-variational inequalities

Abstract

We propose a new formulation of the Karush–Kunt–Tucker conditions of a particular class of quasi-variational inequalities. In order to reformulate the problem we use the Fisher–Burmeister complementarity function and canonical duality theory. We establish the conditions for a critical point of the new formulation to be a solution of the original quasi-variational inequality showing the potentiality of such approach in solving this class of problems. We test the obtained theoretical results with a simple heuristic that is demonstrated on several problems coming from the academy and various engineering applications

RETRACTED: Canonical dual approach for contact mechanics problems with friction

“…In this work we propose a novel canonical duality approach for solving the QVI associated with the contact problem with Coulomb friction by presenting a deeper insight into said application of the theory already presented in [18]. In particular we show that the QVI associated with the problem belongs to a particular class of QVIs called affine quasi-variational inequalities (AQVIs).…”

RETRACTED: Double well potential function and its optimization in the n-dimensional real space: part II

“…All of these functions appear extensively in modeling real-world problems, such as computational biology [127], bio-mechanics, phase transitions [29], filter design [132], location/transportation and networks optimization [129,130], communication and information theory (see [133]), etc. By using the canonical duality-triality theory, these problems can be solved nicely (see [87,[134][135][136][137][138][139][140][141][142][143]). …”

Analytic Solutions to Optimal Control Problems with Constraints

“…The canonical duality theory was developed from nonconvex analysis and mechanics during the last decade (see [9] [10]), and has shown its potential for global optimization and nonconvex nonsmooth analysis [10]- [14]. Meanwhile, we introduce a differential flow for constructing the so-called canonical dual function to deduce some optimality conditions for solving global optimizations, which is shown to extend some corresponding results in canonical duality theory [9]- [11]. In comparison to the previous work mainly focused on simple constraints, we not only discuss linear box constraints, but also the nonlinear sphere constraint.…”