New complexity analysis of a full-Newton step feasible interior-point algorithm for $$P_*(\kappa )$$ P ∗ ( κ ) -LCP

A full-Newton step feasible interior-point algorithm for P∗(κ)-LCP based on a new search direction

“…In this section, we compare the proposed algorithm in this paper with the given algorithm in [30]. We consider the P * (κ)-LCP as follows:…”

“…In all experiments, the algorithms terminate after the duality gap satisfies x T s ≤ 10 −4 . We observe that in Table 1 Algorithm in [30]. Although, in theory, the convergence is not guaranteed for bigger θ values, we performed a MATLAB experiment for θ = 0.05.…”

“…Achache [2], Asadi and Mansouri [4] and Kheirfam [12] presented numerical results on LCPs based on this technique. Later on, Achache [1], Wang and Bai [27,28,29] and Wang et al [30] extended Darvay's algorithm for LO to convex quadratic optimization (CQO), semidefinite optimization (SDO), second-order cone optimization (SOCO), symmetric cone optimization (SCO) and P * (κ)-LCP, respectively. Kheirfam introduced an infeasible IPM for SCO in [13].…”

A new full-NT step interior-point method for circular cone optimization

“…In the 2003s, Darvay [4] introduces a modification in the centering equations xs = µe of the central path by considering ϕ( xs µ ) = ϕ(e), where ϕ : R n + → R n + is assumed to be a smooth function such that ϕ(0) = 0. This direction has become an active area in the past few years for the case ϕ(t) = √ t. For example, the Darvay's results for LO is extended to convex quadratic optimization (CQO) [1], SDO [18], P * (κ)-LCP [21], SOCO [17] and SCO [19]. Very recently, Darvay and Takács [5] introduce another method for characterizing search directions for LO.…”

A generalized direction in interior point method for monotone linear complementarity problems

“…This new direction has become an active subject in the past few years for ϕ(t) = √ t. For instance, the original result that Darvay established for linear programming is extended to convex quadratic programming and monotone LCP in [1,2]. Furthermore in [4,29] the authors extend the result of worst-case polynomial complexity to the wider class of sucient LCPs for FN-IPM. Finally Input: an accuracy parameter > 0 ; a sequence of update parameters {θ k }, 0 < θ k < 1 ∀k ∈ N ; initial values (z 0 , s 0 ) ∈ F + , µ 0 = z 0 s 0 ; 1 z := z 0 , s := s 0 , µ := µ 0 , θ := θ 0 , k := 0 ; 2 while z T s ≥ n do Algorithm 1: Full Newton step IPM (FN-IPM) a method independent of the choice of the initial iterate can be found in [5].…”