Related papers: A quantitative program for Hadwiger's covering con…
This paper deals with the regularization of the sum of functions defined on a locally convex spaces through their closed-convex hulls in the bidual space. Different conditions guaranteeing that the closed-convex hull of the sum is the sum…
Frequent itemsets form a polytope and can be found and analyzed with Linear Programming.
The convex body isoperimetric conjecture in the plane asserts that the least perimeter to enclose given area inside a unit disk is greater than inside any other convex set of area $\pi$. In this note we confirm two cases of the conjecture:…
For closed $k$-Schur Katalan functions $\fg{\lambda}{k}$ with $k$ a positive integer and $\lambda$ a $k$-bounded partition, Blasiak, Morse and Seelinger proposed the alternating dual Pieri rule conjecture and the $k$-branching conjecture.…
We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a…
In this paper, we present sufficient conditions ensuring that the sum of the image of quadratic functions and the nonnegative orthant is convex. The hidden convexity of the trust-region problem with linear inequality constraints is…
Extending classical results on polytopal approximation of convex bodies, we derive asymptotic formulas for the weighted approximation of smooth convex functions by piecewise affine convex functions as the number of their facets tends to…
This paper proposes a non-Gaussian Markov field with a special feature: an explicit partition function. To the best of our knowledge, this is an original contribution. Moreover, the explicit expression of the partition function enables the…
In [BL] in relation to the unsolved Bang's plank problem (1951) we obtained a lower bound for the sum of relevant measures of cylinders covering a given d-dimensional convex body. In this paper we provide the packing counterpart of these…
We define quasiconvex programming, a form of generalized linear programming in which one seeks the point minimizing the pointwise maximum of a collection of quasiconvex functions. We survey algorithms for solving quasiconvex programs either…
The Brunn-Minkowski theory relies heavily on the notion of mixed volumes. Despite its particular importance, even explicit representations for the mixed volumes of two convex bodies in Euclidean space are available only in special cases.…
A polyhedral approximation of a convex body can be calculated by solving approximately an associated multiobjective convex program (MOCP). An MOCP can be solved approximately by Benson type algorithms, which compute outer and inner…
In this paper we study the covering numbers of the space of convex and uniformly bounded functions in multi-dimension. We find optimal upper and lower bounds for the $\epsilon$-covering number of $\C([a, b]^d, B)$, in the $L_p$-metric, $1…
In this paper, we use the Mordukhovich derivatives to precisely find the covering constants for the metric projection operator onto nonempty closed and convex subsets in uniformly convex and uniformly smooth Banach spaces. We consider three…
We study the most-informative Boolean function conjecture using a differential equation approach. This leads to a formulation of a functional inequality on finite-dimensional random variables. We also develop a similar inequality in the…
This paper provides an unique dual representation of set-valued lower semi-continuous quasiconvex and convex functions. The results are based on a duality result for increasing set valued functions.
This paper develops a correspondence relating convex hulls of fractional functions with those of polynomial functions over the same domain. Using this result, we develop a number of new reformulations and relaxations for fractional…
The concept of illumination bodies studied in convex geometry is used to amend the halfspace depth for multivariate data. The proposed notion of illumination enables finer resolution of the sample points, naturally breaks ties in the…
It is presented the simplest known disproof of the Borsuk conjecture stating that if a bounded subset of n-dimensional Euclidean space contains more than n points, then the subset can be partitioned into n+1 nonempty parts of smaller…
We conjecture a structure formula for the $\mathrm{SU}(r)$ Vafa-Witten partition function for surfaces with holomorphic 2-form. The conjecture is based on $S$-duality and a structure formula for the vertical contribution previously derived…