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Full Newton-Step Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Antre M. Drummer, Ljiljana Miletić
Full Newton-Step Interior-Point Method For Linear Complementarity Problems, Goran Lesaja, Antre M. Drummer, Ljiljana Miletić
Department of Mathematical Sciences Faculty Publications
In this paper we consider an Infeasible Full Newton-step Interior-Point Method (IFNS-IPM) for monotone Linear Complementarity Problems (LCP). The method does not require a strictly feasible starting point. In addition, the method avoids calculation of the step size and instead takes full Newton-steps at each iteration. Iterates are kept close to the central path by suitable choice of parameters. The algorithm is globally convergent and the iteration bound matches the best known iteration bound for these types of methods.
Kernel-Based Interior-Point Methods For Cartesian P*(Κ)-Linear Complementarity Problems Over Symmetric Cones, Goran Lesaja
Kernel-Based Interior-Point Methods For Cartesian P*(Κ)-Linear Complementarity Problems Over Symmetric Cones, Goran Lesaja
Department of Mathematical Sciences Faculty Publications
We present an interior point method for Cartesian P*(k)-Linear Complementarity Problems over Symmetric Cones (SCLCPs). The Cartesian P*(k)-SCLCPs have been recently introduced as the generalization of the more commonly known and more widely used monotone SCLCPs. The IPM is based on the barrier functions that are defined by a large class of univariate functions called eligible kernel function which have recently been successfully used to design new IPMs for various optimization problems. Eligible barrier (kernel) functions are used in calculating the Nesterov-Todd search directions and the default step-size which leads to a very good complexity results for the method. For …
Unified Analysis Of Kernel-Based Interior-Point Methods For P *(Κ)-Lcp, Goran Lesaja, C. Roos
Unified Analysis Of Kernel-Based Interior-Point Methods For P *(Κ)-Lcp, Goran Lesaja, C. Roos
Department of Mathematical Sciences Faculty Publications
We present an interior-point method for the P∗(κ)-linear complementarity problem (LCP) that is based on barrier functions which are defined by a large class of univariate functions called eligible kernel functions. This class is fairly general and includes the classical logarithmic function and the self-regular functions, as well as many non-self-regular functions as special cases. We provide a unified analysis of the method and give a general scheme on how to calculate the iteration bounds for the entire class. We also calculate the iteration bounds of both long-step and short-step versions of the method for several …