A full step infeasible interior-point method for Cartesian $$P_{*}(\kappa )$$ P ∗ ( κ ) -SCLCP

A new search direction for full-Newton step infeasible interior-point method in linear optimization

“…x + := x + ∆x, y + := y + ∆y, s + := s + ∆s. (12) Furthermore, in each iteration of the algorithm, a quantity is needed to measure how far an iterate is from the central path. We consider the proximity measure defined by…”

“…The author is improved this algorithm so that the algorithm performs only one feasibility step in each iteration and does not need centering steps [20]. Kheirfam [11,12,13,14] extended the algorithm proposed in [20] to HLCP, the Cartesian P * (κ)-LCP, the convex quadratic symmetric cone optimization (CQSCO) and SO. By considering the AET technique based on the function ψ(t) = t − √ t, Darvay et al [3] have introduced a full-Newton step IPM for LO.…”

An infeasible full NT-step interior point method for circular optimization

“…Each main iteration of the aforementioned IIPMs is composed of one so-called feasibility step and a several centering steps to get an -optimal solution of the underlying problem. Recently, Roos [23] and Kheirfam [12,13,14] proposed IIPMs for LO, HLCP, the Cartesian P * (κ)-SCLCP and SCO so that their algorithms do not need centering steps and take only one feasibility step in order to get a new iterate close enough to the central path.…”

“…Motivated by Roos [23] and Kheirfam [12,13,14], we present a full-NT step IIPM for CO. Each main iteration of the proposed algorithm is consisted of only one feasibility step. Moreover, we analyze the algorithm and derive the iteration-complexity bound which matches the currently best-known iteration bound for IIPMs.…”

A new search direction for full-Newton step infeasible interior-point method in linear optimization

“…Roos [23] introduced an improved version of the method for LO that does not require centering steps, while the aforementioned methods require several (at most three) centering steps in each (main) iteration. Kheirfam extended this method to HLCP [11], the Cartesian P * (κ)-LCP [12], the convex quadratic symmetric cone optimization (CQSCO) [13] and SO [14]. Kheirfam [7] proposed an infeasible version of the method presented in [4] for SDLCP.…”