In this paper, we introduce the concept of linear v{C}ech closure spaces and establish the properties of open sets in linear v{C}ech closure spaces (Lv{C}CS). Here, we observe that the concept of linearity is preserved by semi-open sets, g-semi open sets, $gamma$-open sets, sgc-dense sets and compact sets in Lv{C}CS. We also discuss the concept of relative v{C}ech closure operator, meet and pro...

Consider the semi-parametric linear regression model Y = ′X+ , where has an unknown distribution F0. The semi-parametric MLE
̃ of under this set-up is called the generalized semi-parametric MLE(GSMLE).Although the GSML estimation of the linear regression model is statistically appealing, it has never been attempted due to difficulties with obtaining the GSML estimates of and F until recent work...

Any linear (ordinary or semi-infinite) optimization problem, and also its dual problem, can be classified as either inconsistent or bounded or unbounded, giving rise to nine duality states, three of them being precluded by the weak duality theorem. The remaining six duality states are possible in linear semi-infinite programming whereas two of them are precluded in linear programming as a conse...

Continuous Event Graphs (CEGs), a subclass of Continuous Petri Nets, are defined as the limiting cases of timed event graphs and Timed Event Multigraphs. A set of dioid algebraic linear equations will be inferred as a novel method of analyzing a special class of CEG, if treated the cumulated token consumed by transitions as state-variables, endowed the monotone nondecreasing functions pointwise...

A branch-and-cut algorithm for solving linear problems with continuous separable piecewise linear cost functions was developed in 2005 by Keha et. al. This algorithm is based on valid inequalities for an SOS2 based formulation of the problem. In this paper we study the extension of the algorithm to the case where the cost function is only lower semicontinuous. We extend the SOS2 based formulati...

In this paper, we presented a novel semi-supervised one-class classification algorithm which assumes that class is linearly separable from other elements. We proved theoretically that class is linearly separable if and only if it is maximal by probability within the sets with the same mean. Furthermore, we presented an algorithm for identifying such linearly separable class utilizing linear pro...

This paper deals with stability properties of the feasible set of linear inequality systems having a …nite number of variables and an arbitrary number of constraints. Several types of perturbations preserving consistency are considered, a¤ecting respectively, all of the data, the left-hand side data, or the right-hand side coe¢ cients. Mathematics Subject Classi…cation (2000): Primary : 49K40, ...

We give new facets and valid inequalities for the separable piecewise linear optimization knapsack polytope. We also extend the inequalities to the case in which some of the variables are semi-continuous. In a companion paper [12] we demonstrate the efficiency of the inequalities when used as cuts in a branch-and-cut scheme.

We discuss data-driven morphological segmentation, in which word forms are segmented into morphs, the surface forms of morphemes. Our focus is on a lowresource learning setting, in which only a small amount of annotated word forms are available for model training, while unannotated word forms are available in abundance. The current state-of-art methods 1) exploit both the annotated and unannota...

Semi-infinite linear programs often arise as the limit of a sequence of approximating linear programs. Hence, studying the behavior of extensions of linear programming algorithms to semi-infinite problems can yield valuable insight into the behavior of the underlying linear programming algorithm when the number of constraints or the number of variables is very large. In this paper, we study the...