We consider a challenging resource allocation problem arising in mobile wireless communications. The goal is to allocate the available channels and power in a so-called OFDMA system, in order to maximise the transmission rate, subject to quality of service (QoS) constraints. Standard MINLP software struggled to solve even small instances of this problem. Using outer … Read more
To develop practical and efficient scenario tree reduction methods, we introduce a new methodology which allows for changing node values, and an easy-to-calculate distance function to measure the difference between two scenario trees. Based on minimizing the new distance, we first construct a primitive scenario tree reduction model which also minimizes the Wasserstein distance between … Read more
Nesterov’s accelerated gradient method for minimizing a smooth strongly convex function $f$ is known to reduce $f(\x_k)-f(\x^*)$ by a factor of $\eps\in(0,1)$ after $k\ge O(\sqrt{L/\ell}\log(1/\eps))$ iterations, where $\ell,L$ are the two parameters of smooth strong convexity. Furthermore, it is known that this is the best possible complexity in the function-gradient oracle model of computation. The … Read more
The essential structure of the mixed–integer programming formulation for chance–constrained program (CCP) is the intersection of multiple mixing sets with a $0-1$ knapsack. To improve our computational capacity on CCP, an underlying substructure, the (single) mixing set with a $0-1$ knapsack, has received substantial attentions recently. In this study, we consider a CCP problem with … Read more
In this paper, we propose a new customized proximal point algorithm for linearly constrained convex optimization problem, and further use it to solve the separable convex optimization problem with linear constraints. Which is different to the existing customized proximal point algorithms, the proposed algorithm does not involve any relaxation step but still ensure the convergence. … Read more
Mathematical programs with equilibrium (or complementarity) constraints, MPECs for short, are a difficult class of constrained optimization problems. The feasible set has a very special structure and violates most of the standard constraint qualifications (CQs). Thus, the Karush-Kuhn-Tucker (KKT) conditions are not necessarily satisfied by minimizers and the convergence assumptions of many methods for solving … Read more
This paper discusses several (sub)gradient methods attaining the optimal complexity for smooth problems with Lipschitz continuous gradients, nonsmooth problems with bounded variation of subgradients, weakly smooth problems with H\”older continuous gradients. The proposed schemes are optimal for smooth strongly convex problems with Lipschitz continuous gradients and optimal up to a logarithmic factor for nonsmooth problems … Read more
We apply novel inner-iteration preconditioned Krylov subspace methods to the interior-point algorithm for linear programming (LP). Inner-iteration preconditioners recently proposed by Morikuni and Hayami enable us to overcome the severe ill-conditioning of linear equations solved in the final phase of interior-point iterations. The employed Krylov subspace methods do not suffer from rank-deficiency and therefore no … Read more
The International Space Station poses very challenging issues from the logistic point of view. Its on-orbit stay is to be significantly extended in the near future and ever increasing experimental activity in microgravity is expected, giving rise to a renewed interest in the related optimization aspects. A permanent logistic support is necessary to guarantee its … Read more
This chapter examines the problem of packing tetris-like items, orthogonally, with the possibility of rotations, into a convex domain, in the presence of additional conditions. An MILP (Mixed Integer Linear Programming) and an MINLP (Mixed Integer Nonlinear Programming) models, previously studied by the author, are surveyed. An efficient formulation of the objective function, aimed at … Read more