We propose an entire space polynomial-time algorithm for linear programming. First, we give a class of penalty functions on entire space for linear programming by which the dual of a linear program of standard form can be converted into an unconstrained optimization problem. The relevant...

Given a graph G=(V, E), a set of vertices <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${S \subseteq V}$$</EquationSource> </InlineEquation> covers a vertex <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${v \in V}$$</EquationSource> </InlineEquation> if the edge-connectivity between S and v is at least a given number k. Vertices in S are called sources. The maximum-cover source location problem, which is a variation of the source location problem,...</equationsource></inlineequation></equationsource></inlineequation>

The x-and-y-axes travelling salesman problem forms a special case of the Euclidean TSP, where all cities are situated on the x-axis and on the y-axis of an orthogonal coordinate system of the Euclidean plane. By carefully analyzing the underlying combinatorial and geometric structures, we show...

We consider a pairwise kidney exchange model. Roth et al. (2005) define priority matchings of the model and introduce a mechanism to derive them. In this paper, we re-examine the priority matching. First, we consider a general priority ordering where multiple patients may hold equal priority. We...

<Para ID="Par1">In this paper an exterior point polynomial time algorithm for convex quadratic programming problems is proposed. We convert a convex quadratic program into an unconstrained convex program problem with a self-concordant objective function. We show that, only with duality, the Path-following...</para>

Given a graph G=(V, E), a set of vertices $${S \subseteq V}$$ covers a vertex $${v \in V}$$ if the edge-connectivity between S and v is at least a given number k. Vertices in S are called sources. The maximum-cover source location problem, which is a variation of the source location problem, is...

Focusing on the testable revealed preference restrictions on the equilibrium manifold, we show that the rationalizability problem is NP-complete. Subsequently, we present a mixed integer programming (MIP) approach to characterize the testable implications of general equilibrium models....

We consider a special case of the directed subgraph homeomorphism or topological minor problem, where the host graph has a specific regular structure. Given an acyclic directed pattern graph, we are looking for a host graph of minimal height which still allows for an embedding. This problem has...

In this paper we investigate a vehicle routing problem motivated by a real-world application in cooperation with the German Automobile Association (ADAC). The general task is to assign service requests to service units and to plan tours for the units such as to minimize the overall cost. The...