We study mixed integer nonlinear programs (MINLP)s that are driven by a collection of indicator variables where each indicator variable controls a subset of the decision variables. An indicator variable, when it is “turned off”, forces some of the decision variables to assume fixed values, and, when it is “turned on”, forces them to belong to a convex set. Many practical MINLPs contain integer ...

In the paper [HK] the notions of an adapted distribution and of a saturated adapted probability space were introduced. The adapted distribution of a random variable on an adapted space (with values in a complete separable metric space) is the natural analogue of the distribution of a random variable on a probability space. An adapted space Ω is saturated if for any random variable x on Ω and pa...

with the expanding demand on application of magnesium alloys in automotive and aerospace industries, robust methods in fatigue characterization of commercially available magnesium alloys with high specific strength is anticipated. in this paper, rotating bending load controlled tests has been studied on specimens machined from an extrusion piece of az31b. due to asymmetric and anisotropic behav...

In this paper, we consider a prototypical convex optimization problem with multi-block variables and separable structures. By adding the Logarithmic Quadratic Proximal (LQP) regularizer suitable proximal parameter to each of first grouped subproblems, develop partial LQP-based Alternating Direction Method Multipliers (ADMM-LQP). The dual variable is updated twice relatively larger stepsizes tha...

We present the design of two dimensional finite impulse response(FIR) signal adapted filter banks for an input signal whose power spectral density is separable. One dimensional FIR filters are designed for each of the separable components using iterative greedy algorithm. The first and last filters in this 2D filter bank are found to be separable and matching closely with ideal ones .The remain...

Fast algorithms for a wide class of non–separable n–dimensional (nD) discrete unitary K– transforms (DKT) are introduced. They need less 1D DKTs than in the case of the classical radix–2 FFT–type approach. The method utilizes a decomposition of the nDK–transform into the product of a new nD discrete Radon transform and of a set of parallel/independ 1D K–transforms. If the nD K–transform has a s...

The classical alternating direction method (ADM) has been well studied in the context of linearly constrained convex programming problems and variational inequalities where both the involved operators and constraints are separable into two parts. In particular, recentness has witnessed a number of novel applications arising in diversified areas (e.g. Image Processing and Statistics), for which ...

Data clustering is a difficult and challenging task, especially when the hidden clusters are of different shapes and non-linearly separable in the input space. This paper addresses this problem by proposing a new method that combines a path-based dissimilarity measure and multi-dimensional scaling to effectively identify these complex separable structures. We show that our algorithm is able to ...

In this paper we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newto...

Conventional methods of solving nonconvex separable programming (NSP) problems by mixed integer programming methods requires adding numerous 0±1 variables. In this work, we present a new method of deriving the global optimum of a NSP program using less number of 0±1 variables. A separable function is initially expressed by a piecewise linear function with summation of absolute terms. Linearizin...