Algorithms in Discrete Convex Analysis
نویسنده
چکیده
This is a survey of algorithmic results in the theory of “discrete convex analysis” for integer-valued functions defined on integer lattice points. The theory parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, the Fenchel min-max duality, and separation theorems. The technical development is based on matroid-theoretic concepts, in particular, submodular functions and exchange axioms. key words: discrete convex analysis, matroid, L-convex function, M-convex function
منابع مشابه
Comparison of Simulated Annealing and Electromagnetic Algorithms for Solution of Extended Portfolio Model
This paper presents two meta-heuristic algorithms to solve an extended portfolio selection model. The extended model is based on the Markowitz's Model, aiming to minimize investment risk in a specified level of return. In order to get the Markowitz model close to the real conditions, different constraints were embedded on the model which resulted in a discrete and non-convex solution space. ...
متن کاملMATHEMATICAL ENGINEERING TECHNICAL REPORTS Discrete L-/M-Convex Function Minimization Based on Continuous Relaxation
We consider the problem of minimizing a nonlinear discrete function with L-/M-convexity proposed in the theory of discrete convex analysis. For this problem, steepest descent algorithms and steepest descent scaling algorithms are known. In this paper, we use continuous relaxation approach which minimizes the continuous variable version first in order to find a good initial solution of a steepes...
متن کاملA 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 continuous DC theory are exported to the discrete DC theory with the use of discrete convex analysis. A discrete DC algorithm, which is a discrete analogue of the continuous DC algorithm (Concave-Convex Procedure in ma...
متن کاملNon-homogeneous continuous and discrete gradient systems: the quasi-convex case
In this paper, first we study the weak and strong convergence of solutions to the following first order nonhomogeneous gradient system $$begin{cases}-x'(t)=nablaphi(x(t))+f(t), text{a.e. on} (0,infty)\x(0)=x_0in Hend{cases}$$ to a critical point of $phi$, where $phi$ is a $C^1$ quasi-convex function on a real Hilbert space $H$ with ${rm Argmin}phineqvarnothing$ and $fin L^1(0...
متن کاملOn new faster fixed point iterative schemes for contraction operators and comparison of their rate of convergence in convex metric spaces
In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.
متن کامل