Related papers: Optimizing Polymatroid Functions
Combinatorial optimization can be described as the problem of finding a feasible subset that maximizes a objective function. The paper discusses combinatorial optimization problems, where for each dimension the set of feasible subsets is…
Constrained submodular set function maximization problems often appear in multi-agent decision-making problems with a discrete feasible set. A prominent example is the problem of multi-agent mobile sensor placement over a discrete domain.…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
We formalize the problem of selecting the optimal set of options for planning as that of computing the smallest set of options so that planning converges in less than a given maximum of value-iteration passes. We first show that the problem…
The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of…
We study a class of combinatorial scheduling problems characterized by a particular type of constraint often associated with electrical power or gas energy. This constraint appears in several practical applications and is expressed as a sum…
Two seemingly unrelated problems, scheduling a multiclass queueing system and minimizing a submodular function, share a rather deep connection via the polymatroid that is characterized by a submodular set function on the one hand and…
Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
Submodular function optimization has numerous applications in machine learning and data analysis, including data summarization which aims to identify a concise and diverse set of data points from a large dataset. It is important to…
We consider the problem of the computation of $\inf_p \theta p$ over the set of exponent pairs $P \ni p$ under linear constraints for a certain class of objective functions $\theta$. An effective algorithm is presented. The output of the…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
We give sublinear-time approximation algorithms for some optimization problems arising in machine learning, such as training linear classifiers and finding minimum enclosing balls. Our algorithms can be extended to some kernelized versions…
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
We study a type of reverse (procurement) auction problems in the presence of budget constraints. The general algorithmic problem is to purchase a set of resources, which come at a cost, so as not to exceed a given budget and at the same…
Nonlinear constrained optimization problems are encountered in many scientific fields. To utilize the huge calculation power of current computers, many mathematic models are also rebuilt as optimization problems. Most of them have…
Constrained submodular function maximization has been used in subset selection problems such as selection of most informative sensor locations. While these models have been quite popular, the solutions Constrained submodular function…
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…