相关论文: A General Regularized Continuous Formulation for t…
We investigate continuous regularization methods for linear inverse problems of static and dynamic type. These methods are based on dynamic programming approaches for linear quadratic optimal control problems. We prove regularization…
Is detecting a $k$-clique in $k$-partite regular (hyper-)graphs as hard as in the general case? Intuition suggests yes, but proving this -- especially for hypergraphs -- poses notable challenges. Concretely, we consider a strong notion of…
We present a continuous nonlinear optimization model for the Spin Glass Problem (SGP), building on a classical result by Rosenberg (1972), which shows that for a class of multilinear polynomial problems the optimal values of the continuous…
We consider the problems of finding a maximum clique in a graph and finding a maximum-edge biclique in a bipartite graph. Both problems are NP-hard. We write both problems as matrix-rank minimization and then relax them using the nuclear…
The maximum likelihood method is the best-known method for estimating the probabilities behind the data. However, the conventional method obtains the probability model closest to the empirical distribution, resulting in overfitting. Then…
Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUE problem in several classes of multiple…
For an optimal control problem, the concept of a strong local infimum is introduce, for which necessary conditions consisting of some family of "maximum principles" are formulated. If a function delivers a strong local minimum in this…
In this paper we present algorithms for several string problems in the Congested Clique model. In the Congested Clique model, $n$ nodes (computers) are used to solve some problem. The input to the problem is distributed among the nodes, and…
The $k$-defective clique model relaxes the strict completeness constraint of the traditional clique by allowing up to $k$ missing edges, providing a robust formulation for detecting cohesive structures in noisy graphs. Consequently, the…
We analyze a potentially risk-averse convex stochastic optimization problem, where the control is deterministic and the state is a Banach-valued essentially bounded random variable. We obtain strong forms of necessary and sufficient…
Recent research on multiple kernel learning has lead to a number of approaches for combining kernels in regularized risk minimization. The proposed approaches include different formulations of objectives and varying regularization…
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…
We investigate a number of recently reported exact algorithms for the maximum clique problem (MCQ, MCR, MCS, BBMC). The program code used is presented and critiqued showing how small changes in implementation can have a drastic effect on…
Trace norm regularization is a widely used approach for learning low rank matrices. A standard optimization strategy is based on formulating the problem as one of low rank matrix factorization which, however, leads to a non-convex problem.…
This contribution extends the Bron Kerbosch algorithm for solving the maximum weight clique problem, where continuous-valued weights are assigned to both, vertices and edges. We applied the proposed algorithm to graph matching problems.
We present a new formulation of the maximum clique problem of a graph in complex space. We start observing that the adjacency matrix A of a graph can always be written in the form A = B B where B is a complex, symmetric matrix formed by…
Motivated by practical applications, recent works have considered maximization of sums of a submodular function $g$ and a linear function $\ell$. Almost all such works, to date, studied only the special case of this problem in which $g$ is…
Diverse inverse problems in imaging can be cast as variational problems composed of a task-specific data fidelity term and a regularization term. In this paper, we propose a novel learnable general-purpose regularizer exploiting recent…
We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning…
We present a continuous formulation of machine learning, as a problem in the calculus of variations and differential-integral equations, in the spirit of classical numerical analysis. We demonstrate that conventional machine learning models…