In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP)
method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we …

In this article we present a general theory of augmented Lagrangian functions for cone
constrained optimization problems that allows one to study almost all known augmented …

In the second part of our study, we introduce the concept of global extended exactness of
penalty and augmented Lagrangian functions, and derive the localization principle in the …

The augmented Lagrange multiplier as an important concept in duality theory for
optimization problems is extended in this paper to generalized augmented Lagrange …

In this two-part study, we develop a general theory of the so-called exact augmented
Lagrangians for constrained optimization problems in Hilbert spaces. In contrast to …

The recent advance of algorithms for nonlinear semi-definite optimization problems, called
NSDPs, is remarkable. Yamashita et al. first proposed a primal-dual interior point method …

We study properties of the central path underlying a nonlinear semidefinite optimization
problem, called NSDP for short. The latest radical work on this topic was contributed by …

In 2020, Yamakawa and Okuno proposed a stabilized sequential quadratic semidefinite
programming (SQSDP) method for solving, in particular, degenerate nonlinear semidefinite …

We propose a primal-dual interior-point method (IPM) with convergence to second-order
stationary points (SOSPs) of nonlinear semidefinite optimization problems, abbreviated as …

The sparse optimization problem has a wide range of applications in image processing,
compressed sensing, and machine learning, etc. It is well known that l1-minimization …