Multi-class classification is an important and challenging research topic with many real-life
applications. The problem is much harder than the classical binary classification, especially …

As a well-known machine learning technique, support vector machine (SVM) with a kernel
function achieves much success in nonlinear binary classification tasks. Recently, some …

Abstract Let f (x)= x^ TAx+ 2a^ Tx+ cf (x)= x TA x+ 2 a T x+ c and h (x)= x^ TBx+ 2b^ Tx+ dh
(x)= x TB x+ 2 b T x+ d be two quadratic functions having symmetric matrices AA and B B …

The p-regularized subproblem (p-RS) is the key content of a regularization technique in
computing a Newton-like step for unconstrained optimization. The idea is to incorporate a …

Twin support vector machine (TSVM) is a very classical and practical classifier for pattern
classification. However, the traditional TSVM has two limitations. Firstly, it uses the L_2-norm …

Given n× nn× n symmetric matrices AA and B, B, Dines in 1941 proved that the joint range
set {(x TA x, x TB x)| x∈ R n}{(x TA x, x TB x)| x∈ R n} is always convex. Our paper is …

The local nonglobal minimizer of the trust-region subproblem, if it exists, is shown to have
the second smallest objective function value among all KKT points. This new property is …

Hidden convex optimization is a class of nonconvex optimization problems that can be
globally solved in polynomial time via equivalent convex programming reformulations. In this …

The local nonglobal minimizer of trust-region subproblem, if it exists, is shown to have the
second smallest objective function value among all KKT points. This new property is …

In this paper, we propose a non-quadratic extension of homogeneous S-lemma under some
conditions. Then we apply the extended homogeneous S-lemma to reveal the hidden …