Community detection is a widely-studied unsupervised learning problem in which the task is to group similar entities together based on observed pairwise entity interactions. This problem has applications in diverse domains such is social network analysis and computational biology. There is a significant amount of literature studying this problem under the assumption that the communities … Read more
We consider the problem of fitting a polynomial function to a set of data points, each data point consisting of a feature vector and a response variable. In contrast to standard polynomial regression, we require that the polynomial regressor satisfy shape constraints, such as monotonicity, Lipschitz-continuity, or convexity. We show how to use semidefinite programming … Read more
The symmetric alternating direction method of multipliers (S-ADMM) is a classical effective method for solving two-block separable convex optimization. However, its convergence may not be guaranteed for multi-block case providing there is no additional assumptions. In this paper, we propose a partial PPa S-ADMM (referred as P3SADMM), which updates the Lagrange multiplier twice with suitable … Read more
We propose a simple projection and rescaling algorithm that finds {\em most interior} solutions to the pair of feasibility problems \[ \text{find} x\in L\cap \R^n_{+} \text{ and } \text{find} \; \hat x\in L^\perp\cap\R^n_{+}, \] where $L$ is a linear subspace of $\R^n$ and $L^\perp$ is its orthogonal complement. The algorithm complements a basic procedure that … Read more
We consider nested variational inequalities consisting in a (upper-level) variational inequality whose feasible set is given by the solution set of another (lower-level) variational inequality. Purely hierarchical convex bilevel optimization problems and certain multi-follower games are particular instances of nested variational inequalities. We present an explicit and ready-to-implement Tikhonov-type solution method for such problems. We … Read more
Urged by the outbreak of the COVID-19 in Italy, this study aims at helping to tackle the spread of the disease by resorting to operations research techniques. In particular, we propose a mathematical program to model the problem of establishing how many diagnostic tests the Italian regions must perform in order to maximize the overall … Read more
First-order operator splitting methods are ubiquitous among many fields through science and engineering, such as inverse problems, signal/image processing, statistics, data science and machine learning, to name a few. In this paper, we study a geometric property of first-order methods when applying to solve non-smooth optimization problems. With the tool of “partial smoothness”, we design … Read more
In this paper, an algorithm is proposed to find the nearest point of a convex cone to a given vector, which is composed of a series of orthogonal projections. Some properties of this algorithm, including the reasonability of implementation, the global convergence property and the finite termination, etc., are obtained. The proposed algorithm is more … Read more
In this paper, a reliable hybrid algorithm for solving convex quadratic minimization problems is presented. At each iteration, two points are computed: first, an auxiliary point $\dot{x}_k$ is generated by performing a gradient step equipped with an optimal steplength, then, the next iterate $x_{k+1}$ is obtained through a weighted sum of $\dot{x}_k$ with the penultimate … Read more
We study structured multi-armed bandits, which is the problem of online decision-making under uncertainty in the presence of structural information. In this problem, the decision-maker needs to discover the best course of action despite observing only uncertain rewards over time. The decision- maker is aware of certain structural information regarding the reward distributions and would … Read more