A Full Nesterov–Todd Step Infeasible Interior-Point Method for Second-Order Cone Optimization

Improved Complexity Analysis of Full Nesterov–Todd Step Feasible Interior-Point Method for Symmetric Optimization

“…The obtained iteration bounds coincide with the ones derived for LO, where n is replaced by r , the rank of EJAs, which are the currently best known iteration bounds for SO. Some other references, related to full step IPMs, without any attempt to be complete, are [12,[20][21][22][23][24].…”

A New Infeasible Interior-Point Method Based on a Non-Coercive Kernel Function with Improved Centering Steps for Second-Order Cone Optimization

“…For a short history of IIPMs and a motivation for using full step methods we refer to [15,16]. Both versions of the method were extended by Gu et al [8], Zangiabadi et al [21] and Kheirfam and Mahdavi-Amiri [10] to symmetric optimization (SCO), SOCO and linear complementarity problem over symmetric cone (SCLCP), respectively. Darvay [5] proposed a full-Newton step IPM based on a new technique for finding search directions for LO.…”

“…In each iteration, the algorithm uses a feasibility step and only one centering step. In fact, our method is an improved version of IIPMs proposed in [4,21].…”

“…The main iteration consists of a so-called feasibility step and one centering step, whereas the earlier versions, in [4,21], needed two additional centering steps. We use a kernel function to induce the feasibility step.…”

Topology Optimization Considering Limit Analysis

“…Second-order cone programming might be viewed as a generalization of the linear programming or a special case of the semidefinite programming [46]. It appeals to limit analysis researchers due to the existence of computationally efficient methods to obtain the solution [47,48,49]. Moreover, the solution is proved to be global and independent of initial steps [46,50].…”