Investigation of optimality conditions has been one the most interesting topics in theory multiobjective optimisation problems (MOP). To derive necessary MOP, we consider assumptions called constraints qualifications. It is recognised that Guignard Constraint Qualification (GCQ) efficient and general assumption for scalar objective problems; however, GCQ does not ensure Karush-Kuhn Tucker (KKT)...

For a long time, the bilevel programming problem has essentially been considered as a special case of mathematical programs with equilibrium constraints (MPECs), in particular when the so-called KKT reformulation is in question. Recently though, this widespread believe was shown to be false in general. In this paper, other aspects of the difference between both problems are revealed as we consi...

This paper proposes a stability verification method for systems controlled by an early terminated first-order method (e.g., an MPC problem approximately solved by a fixed number of iterations of the fast gradient method). The method is based on the observation that each step of the vast majority of first-order methods is characterized by a Karush-Kuhn-Tucker (KKT) system which (provided that al...

The composite Lq (0 < q < 1) minimization problem over a general polyhedron has received various applications in machine learning, wireless communications, image restoration, signal reconstruction, etc. This paper aims to provide a theoretical study on this problem. Firstly, we show that for any fixed 0 < q < 1, finding the global minimizer of the problem, even its unconstrained counterpart, is...

OBJECTIVES To demonstrate initial results using Khan Kinetic Treatment (KKT) as a chronic neck pain treatment and to present pain control mechanistic theory on which the treatment is based. METHODS A self-reported functional assessment, neck pain questionnaire, and pain medication dose were used as outcome measures for 44 matched patients randomly split into 2 groups ("treatment" and "control...

We focus on efficient preconditioning techniques for sequences of KKT linear systems arising from the interior point solution of large convex quadratic programming problems. Constraint Preconditioners (CPs), though very effective in accelerating Krylov methods in the solution of KKT systems, have a very high computational cost in some instances, because their factorization may be the most time-...