In this paper we propose new primal-dual interior point methods (IPMs) for P∗(κ) linear complementarity problems (LCPs) and analyze the iteration complexity of the algorithm. New search directions and proximity measures are defined based on a class of kernel functions, ψ(t) = t 2−1 2 − R t 1 e q “ 1 ξ −1 ” dξ, q ≥ 1. If a strictly feasible starting point is available and the parameter q = log „...

Linear programming is one of the most successful disciplines within the eld of operations research. In its standard form, the linear programming problem calls for nding nonnegative x 1 ;. . .; x n so as to maximize a linear function P n j=1 c j x j subject to a system of linear equations: a 11 x 1 + + a 1n x n = b 1. .. a m1 x 1 + + a mn x n = b m : This problem can be stated in vector notation...

This paper deals with a class of primal-dual interior-point algorithms for semideenite programming (SDP) which was recently introduced by Kojima, Shindoh and Hara 11]. These authors proposed a family of primal-dual search directions that generalizes the one used in algorithms for linear programming based on the scaling matrix X 1=2 S ?1=2. They study three primal-dual algorithms based on this f...

We present a hierarchical model predictive control approach for large-scale systems based on dual decomposition. The proposed scheme allows coupling in both dynamics and constraints between the subsystems and generates a primal feasible solution within a finite number of iterations, using primal averaging and a constraint tightening approach. The primal update is performed in a distributed way ...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

We develop a parameterized Primal-Dual π Learning method based on deep neural networks for Markov decision process with large state space and off-policy reinforcement learning. In contrast to the popular Q-learning and actor-critic methods that are based on successive approximations to the nonlinear Bellman equation, our method makes primal-dual updates to the policy and value functions utilizi...

We present a 1.91457-approximation algorithm for the prize-collecting travelling salesman problem. This is obtained by combining a randomized variant of a rounding algorithm of Bienstock et al. [2] and a primal-dual algorithm of Goemans and Williamson [5].