Related papers: Monomial barrier functions for the box-constrained…
This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…
We study the problem of co-designing control barrier functions (CBF) and linear state feedback controllers for continuous-time linear systems. We achieve this by means of a single semi-definite optimization program. Our formulation can…
This paper presents a piecewise convexification method to approximate the whole approximate optimal solution set of non-convex optimization problems with box constraints. In the process of box division, we first classify the sub-boxes and…
Interior-point methods (IPMs) are a cornerstone of Euclidean convex optimization, due to their strong theoretical guarantees and practical performance. Motivated by scaling problems, recent work by Hirai and the last two authors (FOCS'23)…
A polyhedral convex set optimization problem is given by a set-valued objective mapping from the $n$-dimensional to the $q$-dimensional Euclidean space whose graph is a convex polyhedron. This problem can be seen as the most elementary…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
We investigate how to solve smooth matrix optimization problems with general linear inequality constraints on the eigenvalues of a symmetric matrix. We present solution methods to obtain exact global minima for linear objective functions,…
We propose a new first-order primal-dual optimization framework for a convex optimization template with broad applications. Our optimization algorithms feature optimal convergence guarantees under a variety of common structure assumptions…
Composite convex optimization problems which include both a nonsmooth term and a low-rank promoting term have important applications in machine learning and signal processing, such as when one wishes to recover an unknown matrix that is…
We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
Composite optimization problems involve minimizing the composition of a smooth map with a convex function. Such objectives arise in numerous data science and signal processing applications, including phase retrieval, blind deconvolution,…
We consider an $n$-variate monomial function that is restricted both in value by lower and upper bounds and in domain by two homogeneous linear inequalities. Such functions are building blocks of several problems found in practical…
This paper explores a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraints are known. We allow the objective and constraint function to…
Factor graphs have demonstrated remarkable efficiency for robotic perception tasks, particularly in localization and mapping applications. However, their application to optimal control problems -- especially Model Predictive Control (MPC)…
We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…
This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…
Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…