Results 81 to 90 of about 9,676,389 (199)

A Multilevel Search Algorithm for the Maximization of Submodular Functions [PDF]

We consider the objective function of a simple recourse problem with fixed technology matrix and integer second-stage variables. Separability due to the simple recourse structure allows to study a one-dimensional version instead.
Goldengorin, Boris, Ghosh, Diptesh
core  

Non-Monotone DR-Submodular Function Maximization

, 2017
We consider non-monotone DR-submodular function maximization, where DR-submodularity (diminishing return submodularity) is an extension of submodularity for functions over the integer lattice based on the concept of the diminishing return property ...
Yoshida, Yuichi, Soma, Tasuku
core   +1 more source

Expected Maximization of a Concave Utility Function Under Threshold-Based Activation

Axioms
Maximizing the expected value of a concave and strictly increasing utility function defines a fundamental class of discrete optimization problems. Among them, coverage decision problems with diminishing marginal returns under uncertainty, typically ...
Guangming Li, Yufei Li, Shengjie Chen, Mou Sun, Wushuaijun Zhang   +4 more
doaj   +1 more source

Supermodular Rank: Set Function Decomposition and Optimization

, 2023
We define the supermodular rank of a function on a lattice. This is the smallest number of terms needed to decompose it into a sum of supermodular functions. The supermodular summands are defined with respect to different partial orders.
Montufar, Guido, Seigal, Anna, Sonthalia, Rishi   +2 more
core  

Maximizing General Set Functions by Submodular Decomposition

, 2009
We present a branch and bound method for maximizing an arbitrary set function h mapping 2^V to R. By decomposing h as f-g, where f is a submodular function and g is the cut function of a (simple, undirected) graph G with vertex set V, our original problem is reduced to a sequence of submodular maximization problems.
openaire   +2 more sources

Submodular Function Minimization

, 2011
Funções submodulares aparecem naturalmente em diversas áreas, tais como probabilidade, geometria e otimização combinatória. Pode-se dizer que o papel desempenhado por essas funções em otimização discreta é similar ao desempenhado por convexidade em ...
Simão, Juliana Barby
core   +1 more source

Submodular Functions: from Discrete to Continous Domains [PDF]

, 2018
International audienceSubmodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time.
Bach, Francis, Francis Bach
core   +1 more source

Minimizing a submodular function arising from a concave function [PDF]

, 1999
We consider a class of submodular functions on distributive lattices that are defined in terms of concave functions and modular functions. The minimization of such a submodular function is made in time required for a max-flow computation on an associated
Satoru Fujishige, Satoru Iwata, Iwata, Satoru, Fujishige, Satoru   +3 more
core   +1 more source

A Mazur-Orlicz type theorem for submodular set functions

Journal of Mathematical Analysis and Applications, 1986
Let \({\mathcal L}\) be a lattice of subsets of a given set \(\Omega\) with \(\emptyset \in {\mathcal L}\). A function \(\gamma:{\mathcal L}\to {\mathbb{R}}\cup \{- \infty \}\) is called a submodular (modular) set function if \(\gamma (\emptyset)=0\) and \[ \gamma (A\cup B)+\gamma (A\cap B)\leq (=)\gamma (A)+\gamma (B),\quad A\in {\mathcal L},\quad B ...
openaire   +2 more sources

Shape preserving properties and monotonicity properties of the sequences of Choquet type integral operators

Journal of Numerical Analysis and Approximation Theory, 2018
In this paper, for the univariate Bernstein-Kantorovich-Choquet, Szasz-Kantorovich-Choquet, Baskakov-Kantorovich-Choquet and Bernstein-Durrmeyer-Choquet operators written in terms of the Choquet integrals with respect to monotone and submodular set ...
Sorin Gal
doaj   +2 more sources