scholarly journals Probabilistic tree-based representation for solving minimum cost integer flow problems with nonlinear non-convex cost functions

2020 ◽  
Vol 86 ◽  
pp. 105951
Author(s):  
Behrooz Ghasemishabankareh ◽  
Xiaodong Li ◽  
Melih Ozlen ◽  
Frank Neumann
Keyword(s):  
Minimum Cost ◽  
Cost Functions ◽  
Flow Problems ◽  
Convex Cost ◽  
Integer Flow

Parametric Computation of Minimum-Cost Flows with Piecewise Quadratic Costs

2021 ◽  
Author(s):  
Max Klimm ◽  
Philipp Warode
Keyword(s):  
Matrix Multiplication ◽  
Minimum Cost ◽  
Convex Program ◽  
Cost Functions ◽  
Quadratic Program ◽  
Polynomial Algorithms ◽  
Strictly Convex ◽  
Flow Problems ◽  
Convex Quadratic Program ◽  
Minimum Cost Flows

We develop algorithms solving parametric flow problems with separable, continuous, piecewise quadratic, and strictly convex cost functions. The parameter to be considered is a common multiplier on the demand of all nodes. Our algorithms compute a family of flows that are each feasible for the respective demand and minimize the costs among the feasible flows for that demand. For single commodity networks with homogenous cost functions, our algorithm requires one matrix multiplication for the initialization, a rank 1 update for each nondegenerate step and the solution of a convex quadratic program for each degenerate step. For nonhomogeneous cost functions, the initialization requires the solution of a convex quadratic program instead. For multi-commodity networks, both the initialization and every step of the algorithm require the solution of a convex program. As each step is mirrored by a breakpoint in the output this yields output-polynomial algorithms in every case.

scholarly journals Solving Robust Variants of Integer Flow Problems with Uncertain Arc Capacities

2021 ◽  
Vol 33 (1) ◽  
pp. 77-89
Author(s):  
Marko Špoljarec ◽  
Robert Manger
Keyword(s):  
Flow Problem ◽  
Network Flows ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Approximate Algorithm ◽  
Minimum Cost Flow ◽  
Flow Problems ◽  
Unit Costs ◽  
Minimum Cost Flow Problem ◽  
Integer Flow

This paper deals with robust optimization and network flows. Several robust variants of integer flow problems are considered. They assume uncertainty of network arc capacities as well as of arc unit costs (where applicable). Uncertainty is expressed by discrete scenarios. Since the considered variants of the maximum flow problem are easy to solve, the paper is mostly concerned with NP-hard variants of the minimum-cost flow problem, thus proposing an approximate algorithm for their solution. The accuracy of the proposed algorithm is verified by experiments.

scholarly journals Adaptation of Random Binomial Graphs for Testing Network Flow Problems Algorithms

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1716
Author(s):  
Adrian Marius Deaconu ◽  
Delia Spridon
Keyword(s):  
Network Flow ◽  
Large Scale ◽  
Random Network ◽  
Minimum Cost ◽  
Maximum Flow ◽  
Network Flow Problems ◽  
Commodity Flow ◽  
Vast Number ◽  
Flow Problems ◽  
Execution Speed

Algorithms for network flow problems, such as maximum flow, minimum cost flow, and multi-commodity flow problems, are continuously developed and improved, and so, random network generators become indispensable to simulate the functionality and to test the correctness and the execution speed of these algorithms. For this purpose, in this paper, the well-known Erdős–Rényi model is adapted to generate random flow (transportation) networks. The developed algorithm is fast and based on the natural property of the flow that can be decomposed into directed elementary s-t paths and cycles. So, the proposed algorithm can be used to quickly build a vast number of networks as well as large-scale networks especially designed for s-t flows.

Cournot Equilibrium Uniqueness: At 0 Discontinuous Industry Revenue and Decreasing Price Flexibility

2019 ◽  
Vol 21 (02) ◽  
pp. 1940010 ◽  
Author(s):  
Pierre Von Mouche ◽  
Takashi Sato
Keyword(s):  
Large Class ◽  
Cost Functions ◽  
Uniqueness Problem ◽  
Unique Equilibrium ◽  
Cournot Equilibrium ◽  
Price Function ◽  
Convex Cost ◽  
Equilibrium Uniqueness ◽  
Price Flexibility

We consider the equilibrium uniqueness problem for a large class of Cournot oligopolies with convex cost functions and a proper price function [Formula: see text] with decreasing price flexibility. This class allows for (at [Formula: see text]) discontinuous industry revenue and in particular for [Formula: see text]. The paper illustrates in an exemplary way the Selten–Szidarovszky technique based on virtual backward reply functions. An algorithm for the calculation of the unique equilibrium is provided.

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