11 papers
An Efficient Vertex Retrieval Algorithm for Ball Polyhedra
Marius Costandin
We consider the intersection of equal-radius balls in whose centers lie on a common sphere centered at the origin, with the origin contained in the…
On Efficient Approximation of the Maximum Distance to A Point Over an Intersection of Balls
Beniamin Costandin, Marius Costandin
In this paper we study the NP-Hard problem of maximizing the distance over an intersection of balls to a given point. We expand the results found in \cite{funcos1}, where the autho…
Tight Bounds for the Maximum Distance Over a Polytope to a Given Point
Marius Costandin, Beniamin Costandin
In this paper we study the problem of maximizing the distance to a given point over a polytope . Assuming that the polytope is circumscribed by a known ball we c…
A Quasi-Polynomial Algorithm for Subset-Sum Problems with At Most One Solution
Marius Costandin, Beniamin Costandin
In this paper we study the problem of maximizing the distance to a given point over an intersection of balls. It was already known that this problem can be solved in polynomial tim…
On Maximizing the Distance to a Given Point over an Intersection of Balls II
Marius Costandin
In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general…
A Polynomial Algorithm for Some Relaxed Subset Sum Problems with Real Numbers
Marius Costandin
In this paper we study the subset sum problem with real numbers. Starting from the given problem, we formulate a quadratic maximization problem over a polytope, P, which is eventua…
A FPTAS for the Subset Sum Problem with Real Numbers
Marius Costandin
In this paper we study the subset sum problem with real numbers. Starting from the given problem, we formulate a quadratic maximization problem over a polytope which is eventually…
On Global Maximization of Bounded Hessian Functions over Strongly Convex Domains
Marius Costandin
In this paper we present two frameworks in which global maximization of a bounded hessian function over a strongly convex set can be reduced to convex optimization. The first prese…
Unconstraint minimization of continuous convex functions. Application to LP
Beniamin Costandin, Marius Costandin, Petru Dobra
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper…
Maximizing The Distance To A "Far Enough" Point Over The Intersection Of Hyper-Disks
Marius-Simion Costandin, Bogdan Gavrea, Beniamin Costandin
We present a novel feasibility criteria for the finite intersection of convex sets given by inequalities. This criteria allows us to easily assert the feasibility by analyzing the…
A new proof for the exact values of for
Marius Costandin
We establish a connection between a function and a series representation using a similar technique with that that Euler used to solve the Basel problem. Our result concerns a more…