Related papers: A Unifying Convexification Framework for Chance-Co…

The training of deep neural networks predominantly relies on a combination of gradient-based optimisation and back-propagation for the computation of the gradient. While incredibly successful, this approach faces challenges such as…

Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges…

It is well-known that the McCormick relaxation for the bilinear constraint $z=xy$ gives the convex hull over the box domains for $x$ and $y$. In network applications where the domain of bilinear variables is described by a network polytope,…

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…

This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity…

We investigate mixed-integer second-order conic (SOC) sets with a nonlinear right-hand side in the SOC constraint, a structure frequently arising in mixed-integer quadratically constrained programming (MIQCP). Under mild assumptions, we…

We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection,…

In the biclustering problem, we seek to simultaneously group observations and features. While biclustering has applications in a wide array of domains, ranging from text mining to collaborative filtering, the problem of identifying…

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…

The pooling problem is a classical NP-hard problem in the chemical process and petroleum industries. This problem is modeled as a nonlinear, nonconvex network flow problem in which raw materials with different specifications are blended in…

Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…

Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…

We present a primal-dual algorithmic framework to obtain approximate solutions to a prototypical constrained convex optimization problem, and rigorously characterize how common structural assumptions affect the numerical efficiency. Our…

Constrained bilevel optimization tackles nested structures present in constrained learning tasks like constrained meta-learning, adversarial learning, and distributed bilevel optimization. However, existing bilevel optimization methods…

Although many convex relaxations of clustering have been proposed in the past decade, current formulations remain restricted to spherical Gaussian or discriminative models and are susceptible to imbalanced clusters. To address these…

Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optimization. We introduce the notion of a Lagrangian dual…

We study a tight Bennett-type concentration inequality for sums of heterogeneous and independent variables, defined as a one-dimensional minimization. We show that this refinement, which outperforms the standard known bounds, remains…

Convex clustering has recently garnered increasing interest due to its attractive theoretical and computational properties, but its merits become limited in the face of high-dimensional data. In such settings, pairwise affinity terms that…

In the past years, augmented Lagrangian methods have been successfully applied to several classes of non-convex optimization problems, inspiring new developments in both theory and practice. In this paper we bring most of these recent…

We study distributed composite optimization over networks: agents minimize the sum of a smooth (strongly) convex function, the agents' sum-utility, plus a non-smooth (extended-valued) convex one. We propose a general algorithmic framework…