In this paper, we introduce the notion of a self-concordant convex-concave function, establish basic properties of these functions and develop a path-following interior point method for approximating saddle points of “good enough” convex-concave functions – those which admit natural self-concordant convex-concave regularizations. The approach is illustrated by its applications to developing an ...

Ellipsoid and toroid-shaped articulations for total wrist prostheses were evaluated using computer modeling and laboratory experiments. An ellipsoidal design was found to accommodate greater width of the concave proximal component, resulting in better capture and prosthetic stability than a toroid shape. An ellipsoid articulation also provides greater contact area through the available arc of m...

Abstract John’s fundamental theorem characterizing the largest volume ellipsoid contained in a convex body $K$ $\mathbb{R}^{d}$ has seen several generalizations and extensions. One direction, initiated by V. Milman is to replace ellipsoids positions (affine images) of another $L$. Another, more recent direction consider logarithmically concave functions on instead bodies: we designate some spec...

We consider the maximization of a gross substitutes utility function under budget constraints. This problem naturally arises in applications such as exchange economies in mathematical economics and combinatorial auctions in (algorithmic) game theory. We show that this problem admits a polynomial-time approximation scheme (PTAS). More generally, we present a PTAS for maximizing a discrete concav...

in this study the land surface in western half of hyper-arid lut desert, in south east of iran, which is covered by yardangs, a worldwide typical landform for aeolian erosion, were classified by self organizing maps (som) method. in the first step by using digital elevation model with 10 m resolution and matlab software, 22 morphometric parameters were calculated based on derivative of the surf...

In this paper, we address the problem of maximizing the volume of the intersection of polytopes in R by translation. We show that (1) the dth root of the objective function is concave, thus the problem can be solved oracle polynomial time by ellipsoidal method, and (2) the problem can be solved in strongly polynomial time in dimension two even for non-convex polygons.

Algorithmic methods are developed that guarantee efficient complexity estimates for strongly convex-concave saddle-point problems in the case when one group of variables has a high dimension, while another rather low dimension (up to 100). These based on reducing this type minimization (maximization) problem convex (concave) functional with respect such an approximate value gradient at arbitrar...

We extend the notion of minimal volume ellipsoid containing a convex body in $$\mathbb {R}^{d}$$ to setting logarithmically concave functions. consider vast class functions whose superlevel sets are concentric ellipsoids. For fixed function from this class, we set all its “affine” positions. any log-concave f on {R}^{d},$$ belonging positions, and find one with integral under condition that it ...

The goal of this paper is to introduce the notion of certificates, which verify the accuracy of solutions of computational problems with convex structure. Such problems include minimizing convex functions, variational inequalities with monotone operators, computing saddle points of convex-concave functions, and solving convex Nash equilibrium problems. We demonstrate how the implementation of t...

− The concept of the reflective solar tower is based on inverting the path of the solar rays originating from a heliostat field to a solar receiver that can be placed on the ground. This system is based on the property of a reflective quadric surface to reflect each ray oriented to one of its foci to its second focus. Two shapes of surfaces can be used: one is concave − the ellipsoid, and the o...