Related papers: Convex relaxations for large-scale graphically str…
Existence of solutions to doubly nonlinear equations in reflexive Banach spaces is established by resorting to a global-in-time variational approach inspired by De Giorgi's principle, which characterizes the associated flows as…
We present a new approach for computing approximate global minimizers to a large class of non-local pairwise interaction problems defined over probability distributions. The approach predicts candidate global minimizers, with a recovery…
Deterministic global optimization of nonlinear models is important in many scientific and engineering applications. This framework typically involves repeatedly solving convex relaxations of the nonconvex problem, meaning that the strength…
Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…
We consider the chance-constrained binary knapsack problem (CKP), where the item weights are independent and normally distributed. We introduce a continuous relaxation for the CKP, represented as a non-convex optimization problem, which we…
We analyze optimal transport problems with additional entropic cost evaluated along curves in the Wasserstein space which join two probability measures $m_0,m_1$. The effect of the additional entropy functional results into an elliptic…
Motivated by a geometric problem, we introduce a new non-convex graph partitioning objective where the optimality criterion is given by the sum of the Dirichlet eigenvalues of the partition components. A relaxed formulation is identified…
The 'exact subgraph' approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
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…
As the title suggests, this is the third paper in a series addressing bilevel optimization problems that are governed by the Kantorovich problem of optimal transport. These tasks can be reformulated as mathematical problems with…
We study the convex relaxation of a polynomial optimization problem, maximizing a product of linear forms over the complex sphere. We show that this convex program is also a relaxation of the permanent of Hermitian positive semidefinite…
This paper presents a convex approach to the optimization of a cooperative rendezvous, that is, the problem of two distant spacecraft that simultaneously operate to get closer. Convex programming guarantees convergence towards the optimal…
Sensor network localization problem is to determine the position of the sensor nodes in a network given pairwise distance measurements. Such problem can be formulated as a polynomial minimization via the least squares method. This paper…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Min-max optimization problems arise in several key machine learning setups, including adversarial learning and generative modeling. In their general form, in absence of convexity/concavity assumptions, finding pure equilibria of the…
Stochastic nonconvex optimization problems with nonlinear constraints have a broad range of applications in intelligent transportation, cyber-security, and smart grids. In this paper, first, we propose an inexact-proximal accelerated…
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the…
We introduce a new algorithm for complex image reconstruction with separate regularization of the image magnitude and phase. This optimization problem is interesting in many different image reconstruction contexts, although is nonconvex and…
We establish a geometric condition guaranteeing exact copositive relaxation for the nonconvex quadratic optimization problem under two quadratic and several linear constraints, and present sufficient conditions for global optimality in…
The subspace approximation problem Subspace($k$,$p$) asks for a $k$-dimensional linear subspace that fits a given set of points optimally, where the error for fitting is a generalization of the least squares fit and uses the $\ell_{p}$ norm…