The present methods for obtaining the optimal LewenesteinSanpera decomposition of a mixed state are difficult to handle analytically. We provide a simple analytical expression for the optimal Lewenstein-Sanpera decomposition by using semidefinite programming. Specially, we obtain the optimal Lewenstein-Sanpera decomposition for some examples such as: Bell decomposable state, Iso-concurrence sta...

The Alternating Direction Method of Multipliers (ADMM) has been proved to be effective for solving separable convex optimization subject to linear constraints. In this paper, we propose a Generalized Symmetric ADMM (GS-ADMM), which updates the Lagrange multiplier twice with suitable stepsizes, to solve the multi-block separable convex programming. This GS-ADMM partitions the data into two group...

The alternating direction method (ADM) is classical for solving a linearly constrained separable convex programming problem (primal problem), and it is well known that ADM is essentially the application of a concrete form of the proximal point algorithm (PPA) (more precisely, the Douglas-Rachford splitting method) to the corresponding dual problem. This paper shows that an efficient method comp...

In this paper, the authors solve the two stage stochastic programming with separable objective by obtaining convex polynomial approximations to the convex objective function with an arbitrary accuracy. Our proposed method will be valid for realistic applications, for example, the convex objective can be either non-differentiable or only accessible by Monte Carlo simulations. The resulting polyn...

Dana Kay Nelkin Abstract: Psychopaths pose a puzzle. The pleasure they take in the pain of others suggests that they are the paradigms of blameworthiness, while their psychological incapacities provide them with paradigm excuses on plausible accounts of moral responsibility. I begin by assessing two influential responses: one that claims that psychopaths are morally blameworthy in one sense and...

We develop a method to obtain an optimal solution for a constrained distribution system with several items and multi-retailers. The objective is to determine the procurement frequency as well as the joint shipment interval for each retailer in order to minimize the total costs. The proposed method is applicable to both nested and non-nested policies and ends up with an optimal solution. To solv...

Symbolic regression aims to find a function that best explains the relationship between independent variables and objective value based on given set of sample data. Genetic programming (GP) is usually considered as an appropriate method for problem since it can optimize functional structure coefficients simultaneously. However, convergence speed GP might be too slow large scale problems involve...

We present an approximation algorithm for the NP-hard problem of finding the largest linearly separable subset of examples among a training set. The algorithm uses, incrementally, a Linear Programming procedure. We present numerical evidence of its superiority over the Pocket algorithm used by many neural net constructive algorithms.

In this paper we present an algorithm of quasi-linear complexity for exactly calculating the infimal convolution of convex quadratic functions. The algorithm exactly and simultaneously solves a separable uniparametric family of quadratic programming problems resulting from varying the equality constraint.

The \lambda method" is a well-known method for using integer linear-programming methods to model separable piecewise-linear functions in the context of optimization formulations. We extend the lambda method to the nonseparable case, and use polyhedral methods to strengthen the formulation.