1993] proposed to solve nonlinear complementarity problems by seeking the unconstrained global minima of a new merit function which they called implicit Lagrangian. A crucial point in such an approach is to determine conditions which guarantee that every uncon-strained stationary point of the implicit Lagrangian is a global solution, since standard unconstrained minimization techniques are only...

Frailty is defined as an age-related decline in physiological reserve and increased vulnerability to stress. As frailty a multifaceted condition, there no effective pharmacotherapy for it yet. Ninjin’yoeito (NYT) Kamikihito (KKT), traditional Japanese medicines (Kampo medicines), are promising treating conditions of including fatigue mental anxiety. However, their effects still unclear. In this...

For an inequality system defined by an infinite family of proper convex functions (not necessarily lower semicontinuous), we introduce some new notions of constraint qualifications. Under the new constraint qualifications, we provide necessary and/or sufficient conditions for the KKT rules to hold. Similarly, we provide characterizations for constrained minimization problems to have total Lagra...

We propose a variant of the classical augmented Lagrangian method for constrained optimization problems in Banach spaces. Our theoretical framework does not require any convexity or second-order assumptions and allows the treatment of inequality constraints with infinite-dimensional image space. Moreover, we discuss the convergence properties of our algorithm with regard to feasibility, global ...

Constraint qualifications (CQ) are assumptions on the algebraic description of the feasible set of an optimization problem that ensure that the KKT conditions hold at any local minimum. In this work we show that constraint qualifications based on the notion of constant rank can be understood as assumptions that ensure that the polar of the linear approximation of the tangent cone, generated by ...

Computing the chromatic number of a graph is an NP-hard problem. For random graphs and some other classes of graphs, estimators of the expected chromatic number have been well studied. In this paper, a new 0–1 integer programming formulation for the graph coloring problem is presented. The proposed new formulation is used to develop a method that generates graphs of known chromatic number by us...

Using variational analysis techniques, we study convex-composite optimization problems. In connection with such a problem, we introduce several new notions as variances of the classical KKT conditions. These notions are shown to be closely related to the notions of sharp or weak sharp solutions. As applications, we extend some results on metric regularity of inequalities from the convex case to...