Related papers: Nonlinear Matroid Optimization and Experimental De…
Submodular maximization under matroid and cardinality constraints are classical problems with a wide range of applications in machine learning, auction theory, and combinatorial optimization. In this paper, we consider these problems in the…
A Lagrange multiplier theorem is derived for the case of an imprecise objective function and a precise constraint. The proof uses methods of analysis which deal in a direct, algebraic way with imprecisions. They include imprecise…
A number of recent results on optimization problems involving submodular functions have made use of the multilinear relaxation of the problem. These results hold typically in the value oracle model, where the objective function is…
Maximizing monotone submodular functions under a matroid constraint is a classic algorithmic problem with multiple applications in data mining and machine learning. We study this classic problem in the fully dynamic setting, where elements…
We consider a problem of optimizing convex functionals over matroid bases. It is richly expressive and captures certain quadratic assignment and clustering problems. While generally NP-hard, we show it is polynomial time solvable when a…
Consider the task of matrix estimation in which a dataset $X \in \mathbb{R}^{n\times m}$ is observed with sparsity $p$, and we would like to estimate $\mathbb{E}[X]$, where $\mathbb{E}[X_{ui}] = f(\alpha_u, \beta_i)$ for some Holder smooth…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
A class of algorithms for the solution of discrete material optimization problems in electromagnetic applications is discussed. The idea behind the algorithm is similar to that of the sequential programming. However, in each major iteration…
Like most multiobjective combinatorial optimization problems, biobjective optimization problems on matroids are in general intractable and their corresponding decision problems are in general NP-hard. In this paper, we consider biobjective…
Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient…
We consider the problem of using experimental time-series data for parameter estimation in nonlinear ordinary differential equations, focusing on the case where the data is noisy, sparse, irregularly sampled, includes multiple experiments,…
We present an optimal, combinatorial 1-1/e approximation algorithm for monotone submodular optimization over a matroid constraint. Compared to the continuous greedy algorithm (Calinescu, Chekuri, Pal and Vondrak, 2008), our algorithm is…
We analyze general model selection procedures using penalized empirical loss minimization under computational constraints. While classical model selection approaches do not consider computational aspects of performing model selection, we…
This thesis is basically devoted to matroids -- fundamental structure of combinatorial optimization -- though some of our results concern simplicial complexes, or Euclidean spaces. We study old and new problems for these structures, with…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
We propose an algebraic combinatorial method for solving large sparse linear systems of equations locally - that is, a method which can compute single evaluations of the signal without computing the whole signal. The method scales only in…