Robust and ∞ Solutions of Linear Inequalities

Infeasible linear inequalities appear in many disciplines. In this paper we investigate the 1 and ∞ solutions of such systems in the presence of uncertainties in the problem data. We give equivalent linear programming formulations for the robust problems. Finally, several illustrative numerical examples using the cvx software package are solved showing the importance of the robust model in the presence of uncertainties in the problem data

An ADMM-Factorization Algorithm for Low Rank Matrix Completion

In this paper, we propose an Alternating Direction Method of Multipliers (ADMM) based algorithm that is taking advantage of factorization for the fixed rank matrix completion problem. The convergence of the proposed algorithm to the KKT point is discussed. Finally, on several classes of test problems, its efficiency is compared with several efficient algorithms from the literature

A New HPM for Integral Equations

Homotopy perturbation method is an effective method for obtaining exact solutions of integral equations. However, it might perform poorly on ill-posed integral equations. In this paper, we introduce a new version of the homotopy perturbation method that efficiently solves ill-posed integral equations. Finally, several numerical examples, including a system of integral equations, are presented to demonstrate the efficiency of the new method

A Generalized Newton-Penalty Algorithm for Large Scale Ill-Conditioned Quadratic Problems

Large scale quadratic problems arise in many real world applications. It is quite often that the coefficient matrices in these problems are ill-conditioned. Thus, if the problem data are available even with small error, then solving them using classical algorithms might result to meaningless solutions. In this short paper, we propose an efficient generalized Newton-penalty algorithm for solving these problems. Our computational results show that our new simple algorithm is much faster and better than the approach of Rojas et al. (2000), which requires parameter tuning for different problems

Optimal Correction of Infeasible Systems in the Second Order Conic Linear Setting

In this paper we consider correcting infeasibility in a second order conic linear inequality by minimal changes in the problem data. Under certain conditions, it is proved that the minimal correction can be done by solving a lower dimensional convex problem. Finally, several examples are presented to show the efficiency of the new approach

Robust Multi-Objective Facility Location Model of Closed-Loop Supply Chain Network under Interval Uncertainty

In this paper, we consider a supply chain network that includes multiple plants, collection centers, demand markets, and products, where a multi-objective mixed integer programming model has been developed to minimize cost and maximize some environmental issues by Amin and Zhang (2013a). Due to the uncertainty of the demands and returns, the robust counterpart of the model is discussed under interval uncertainty. According to some numerical results, the percentage changes of robust and stochastic models are compared relative to deterministic models in different cases. The numerical results show that the robust model in comparison with the stochastic programming model gives a closer fit to the results of the deterministic model