The global convergence of ADMM for convex problems was given by He and Yuan in [5] under the variation inequality framework. However, since our optimization problem is non-convex, the convergence analysis for ADMM needs additional conditions. In non-convex optimization, convergence to a stationary point (local minimum) is the best convergence property that we can hope for. By imposing some cond...

We consider optimality systems of Karush-Kuhn-Tucker (KKT) type, which arise, for example, as primal-dual conditions characterizing solutions of optimization problems or variational inequalities. In particular, we discuss error bounds and Newton-type methods for such systems. An exhaustive comparison of various regularity conditions which arise in this context is given. We obtain a new error bo...

We consider a linear complementarity problem (LCP) arisen from the Arrow-Debreu-Leontief competitive economy equilibrium where the LCP coefficient matrix is symmetric. We prove that the decision problem, to decide whether or not there exists a complementary solution, is NP-complete. Under certain conditions, an LCP solution is guaranteed to exist and we present a fully polynomial-time approxima...

In this paper, we consider using the neural networks to efficiently solve the second-order cone constrained variational inequality (SOCCVI) problem. More specifically, two kinds of neural networks are proposed to deal with the Karush-Kuhn-Tucker (KKT) conditions of the SOCCVI problem. The first neural network uses the FischerBurmeister (FB) function to achieve an unconstrained minimization whic...

The Fisher discriminant analysis (FDA) is a common technique for binary classification. A parametrized extension, which we call the extended FDA, has been introduced from the viewpoint of robust optimization. In this work, we first give a new probabilistic interpretation of the extended FDA. We then develop algorithms for solving an optimization problem that arises from the extended FDA: comput...

In this report we describe how continuation methods can be used for the numerical treatment of multi-objective optimization problems (MOPs): starting with a given Karush-Kuhn-Tucker point (KKTpoint) x̃ of an MOP, these techniques can be applied to detect further KKT-points in the neighborhood of x̃. In the next step, again further points are computed starting with these new-found KKT-points, and ...

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...

A popular technique of designing multiple-input multiple-output (MIMO) communication systems relies on optimizing the positive semidefinite covariance matrix at source. In this paper, a unified MIMO optimization framework based Karush-Kuhn-Tucker (KKT) conditions is proposed. framework, with aid theory, <xref ref-type="theorem" rid="theorem1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns...