Concave Mixed-Integer Quadratic Programming is the problem of minimizing a concave quadratic polynomial over the mixed-integer points in a polyhedral region. In this work we describe two algorithms that find an -approximate solution to a Concave Mixed-Integer Quadratic Programming problem. The running time of the proposed algorithms is polynomial in the size of the problem and in 1/ , provided ...

A game with single-valued best-replies and a unique PSNE is a best-reply potential game if and only if the sequential best-reply dynamics converge (Cournot stability). If the PSNE is not unique, convergence to the set of equilibria is still ensured. It follows, for example, that (a) any strictly quasi-concave supermodular game with a unique PSNE is a best-reply potential game, (b) any strictly ...

We study the one-warehouse multi-retailer (OWMR) problem under deterministic dynamic demand and concave batch order costs, where order batches have an identical capacity and the order cost function for each facility is concave within the batch. Under appropriate assumptions on holding cost structure, we obtain lower bounds via a decomposition that splits the two-echelon problem into single-faci...

Efficient sampling, integration and optimization algorithms for logconcave functions [BV04,KV06,LV06a] rely on the good isoperimetry of these functions. We extend this to show that −1/(n− 1)-concave functions have good isoperimetry, and moreover, using a characterization of functions based on their values along every line, we prove that this is the largest class of functions with good isoperime...

Unstructured tetrahedral grids are a common data representation of three-dimensional scalar fields. For convex unstructured meshes efficient rendering methods are known. For concave or cyclic meshes, however, a significant overhead is required to sort the grid cells in back to front order. In this paper we apply methods known from computational geometry to transform concave into convex grids. W...

In the last lecture we discussed applications of log concavity of real rooted polynomials in designing a deterministic approximation algorithm for permanent. We also introduced the class H-stable polynomial. Recall that a polynomial p(z1, . . . , zn) is H -stable if p(z1, . . . , zn) 6= 0 whenever =zi > 0 for all i. In the last lecture we saw that any univariate H-stable polynomial (with real c...

Minimum concave Cost Network Flow Problems (MCNFPs) arise naturally in many practical applications such as communication, transportation, distribution, and manufacturing, due to economic considerations. In addition, it has been shown that every MCNFP with general nonlinear cost functions can be transformed into a concave MCNFP on an expanded network. It must also be noted, that multiple source ...

We calculate genus distribution formulas for several families of ring-like graphs and prove that they are log-concave. The graphs in each of our ring-like families are obtained by applying the self-bar-amalgamation operation to the graphs in a linear family (linear in the sense of Stahl). That is, we join the two root-vertices of each graph in the linear family. Although log-concavity has been ...

We consider a novel sub-class of log-location-scale models for survival and reliability data formed by restricting the density of the underlying location-scale distribution to be log-concave. These models display a number of attractive properties. We particularly explore the shapes of the hazard functions of these, LLSLC, models. A relatively elegant, if partial, theory of hazard shape arises u...

This paper is to characterize L-concavities and L-convexities via some derived forms of relations operators. Specifically, notions L-concave internal relation space hull are introduced. It proved that the category L-concave
 spaces isomorphic spaces. Also, L-convex enclosed