Minimizing a convex function over the integral points of a bounded convex set is polynomial in fixed dimension (Grötschel et al., 1988). We provide an alternative, short, and geometrically motivated proof of this result. In particular, we present an oracle-polynomial algorithm based on a mixed integer linear optimization oracle
Multiobjective mixed integer convex optimization refers to mathematical programming problems where m...
Given a convex function $f$ on $\mathbb{R}^n$ with an integer minimizer, we show how to find an exac...
Many problems in economics, statistics and numerical analysis can be formulated as the optimization ...
Minimizing a convex function over the integral points of a bounded convex set is polynomial in fixed...
In this paper, we address the problem of minimizing a convex function f over a convex set, with the ...
We give a simple and natural method for computing approximately optimal solutions for minimizing a c...
Given a separation oracle $\mathsf{SO}$ for a convex function $f$ that has an integral minimizer ins...
We extend in two ways the standard Karush–Kuhn–Tucker optimality conditions to problems with a conve...
Technical Report #1664, Computer Sciences Department, University of Wisconsin-Madison, 2009.This pap...
We introduce a concept that generalizes several different notions of a “centerpoint” in the literatu...
The problem of optimizing multivariate scalar polynomial functions over mixed-integer points in poly...
We consider geometric approaches that assist in the solution process of mixed-integer nonlinear prog...
In this article we study convex integer maximization problems with com-posite objective functions of...
AbstractWe study the minimization of an M-convex function introduced by Murota. It is shown that any...
Multiobjective mixed integer convex optimization refers to mathematical programming problems where m...
Given a convex function $f$ on $\mathbb{R}^n$ with an integer minimizer, we show how to find an exac...
Many problems in economics, statistics and numerical analysis can be formulated as the optimization ...
Minimizing a convex function over the integral points of a bounded convex set is polynomial in fixed...
In this paper, we address the problem of minimizing a convex function f over a convex set, with the ...
We give a simple and natural method for computing approximately optimal solutions for minimizing a c...
Given a separation oracle $\mathsf{SO}$ for a convex function $f$ that has an integral minimizer ins...
We extend in two ways the standard Karush–Kuhn–Tucker optimality conditions to problems with a conve...
Technical Report #1664, Computer Sciences Department, University of Wisconsin-Madison, 2009.This pap...
We introduce a concept that generalizes several different notions of a “centerpoint” in the literatu...
The problem of optimizing multivariate scalar polynomial functions over mixed-integer points in poly...
We consider geometric approaches that assist in the solution process of mixed-integer nonlinear prog...
In this article we study convex integer maximization problems with com-posite objective functions of...
AbstractWe study the minimization of an M-convex function introduced by Murota. It is shown that any...
Multiobjective mixed integer convex optimization refers to mathematical programming problems where m...
Given a convex function $f$ on $\mathbb{R}^n$ with an integer minimizer, we show how to find an exac...
Many problems in economics, statistics and numerical analysis can be formulated as the optimization ...
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