Discrete convex analysis
K Murota - Mathematical Programming, 1998 - Springer
A theory of “discrete convex analysis” is developed for integer-valued functions defined on
integer lattice points. The theory parallels the ordinary convex analysis, covering discrete …
integer lattice points. The theory parallels the ordinary convex analysis, covering discrete …
Discrete convex analysis: A tool for economics and game theory
K Murota - arXiv preprint arXiv:2212.03598, 2022 - arxiv.org
This paper presents discrete convex analysis as a tool for economics and game theory.
Discrete convex analysis is a new framework of discrete mathematics and optimization …
Discrete convex analysis is a new framework of discrete mathematics and optimization …
Discrete-convex-analysis-based framework for warm-starting algorithms with predictions
Augmenting algorithms with learned predictions is a promising approach for going beyond
worst-case bounds. Dinitz, Im, Lavastida, Moseley, and Vassilvitskii~(2021) have …
worst-case bounds. Dinitz, Im, Lavastida, Moseley, and Vassilvitskii~(2021) have …
Rethinking Warm-Starts with Predictions: Learning Predictions Close to Sets of Optimal Solutions for Faster $\textL $-/$\textL^♮ $-Convex Function Minimization
An emerging line of work has shown that machine-learned predictions are useful to warm-
start algorithms for discrete optimization problems, such as bipartite matching. Previous …
start algorithms for discrete optimization problems, such as bipartite matching. Previous …
Robust budget allocation via continuous submodular functions
The optimal allocation of resources for maximizing influence, spread of information or
coverage, has gained attention in the past years, in particular in machine learning and data …
coverage, has gained attention in the past years, in particular in machine learning and data …
Gross substitutes condition and discrete concavity for multi-unit valuations: a survey
Efficient allocation of indivisible goods is an important problem in mathematical economics
and operations research, where the concept of Walrasian equilibrium plays a fundamental …
and operations research, where the concept of Walrasian equilibrium plays a fundamental …
Assemble‐to‐Order inventory management via stochastic programming: Chained BOMs and the M‐System
We study an inventory management mechanism that uses two stochastic programs (SPs),
the customary one‐period assemble‐to‐order (ATO) model and its relaxation, to conceive …
the customary one‐period assemble‐to‐order (ATO) model and its relaxation, to conceive …
L-convexity on graph structures
H Hirai - Journal of the Operations Research Society of Japan, 2018 - jstage.jst.go.jp
In this paper, we study classes of discrete convex functions: submodular functions on
modular semilattices and L-convex functions on oriented modular graphs. They were …
modular semilattices and L-convex functions on oriented modular graphs. They were …
A framework of discrete DC programming by discrete convex analysis
A theoretical framework of difference of discrete convex functions (discrete DC functions)
and optimization problems for discrete DC functions is established. Standard results in …
and optimization problems for discrete DC functions is established. Standard results in …
Algorithms for L-convex function minimization: Connection between discrete convex analysis and other research fields
A Shioura - Journal of the Operations Research Society of Japan, 2017 - jstage.jst.go.jp
L-convexity is a concept of discrete convexity for functions defined on the integer lattice
points, and plays a central role in the framework of discrete convex analysis. In this paper …
points, and plays a central role in the framework of discrete convex analysis. In this paper …