A large-step infeasible-interior-point method is proposed for solving P∗(κ)-matrix linear complementarity problems. It is new even for monotone LCP. The algorithm generates points in a large neighborhood of an infeasible central path. Each iteration requires only one matrix factorization. If the problem is solvable, then the algorithm converges from arbitrary positive starting points. The compu...

This paper considers the problem of Bayesian optimization for systems with safety-critical constraints, where both objective function and constraints are unknown, but can be observed by querying system. In applications, system at an infeasible point have catastrophic consequences. Such require a safe learning framework, such that performance optimized while satisfying high probability. this we ...

This paper studies the limiting behavior of weighted infeasible central paths for semidefinite programming obtained from centrality equations of the form XS + SX = 2νW , where W is a fixed positive definite matrix and ν > 0 is a parameter, under the assumption that the problem has a strictly complementary primal–dual optimal solution. We present a different and simpler proof than the one given ...

In this paper, we propose primal-dual potential-reduction algorithms which can start from an infeasible interior point. We rst describe two such algorithms and show that both are polynomial-time bounded. One of the algorithms decreases the Tanabe-Todd-Ye primal-dual potential function by a constant at each iteration under the condition that the duality gap decreases by at most the same ratio as...

A modiied predictor-corrector algorithm is proposed for solving monotone linear complementarity problems from infeasible starting points. The algorithm terminates in O(nL) steps either by nding a solution or by determining that the problem is not solvable. The complexity of the algorithm depends on the quality of the starting point. If the problem is solvable and if a certain measure of feasibi...

We present a new full Nesterov and Todd step infeasible interior-point algorithm for semi-definite optimization. The algorithm decreases the duality gap and the feasibility residuals at the same rate. In the algorithm, we construct strictly feasible iterates for a sequence of perturbations of the given problem and its dual problem. Every main iteration of the algorithm consists of a feasibility...

This paper analyzes sequences generated by infeasible interior point methods. In convex and nonconvex settings, we prove that moving the primal feasibility at the same rate as complementarity will ensure that the Lagrange multiplier sequence will remain bounded, provided the limit point of the primal sequence has a Lagrange multiplier, without constraint qualification assumptions. We also show ...

In this paper, the authors describe and establish the convergence of a new iterative method for solving the (nonmonotone) nonlinear complementarity problem (NCP). The method utilizes ideas from two distinct approaches for solving this problem and combines them into one unified framework. One of these is the infeasible-interior-point approach that computes an approximate solution to the NCP by s...

We propose a primal-dual infeasible-interior-point path-following algorithm for solving semideenite programming (SDP) problems. If the problem has a solution, then the algorithm is globally convergent. If the starting point is feasible or close to being feasible , the algorithms nds an optimal solution in at most O(p nL) iterations. If the starting point is large enough then the algorithm termi...

We present an improved version of an infeasible interior-point method for linear optimization published in 2006. In the earlier version each iteration consisted of one so-called feasibility step and a few – at most three – centering steps. In this paper each iteration consists of only a feasibility step, whereas the iteration bound improves the earlier bound by a factor 2 √ 2. The improvements ...