Related papers: CVXR: An R Package for Disciplined Convex Optimiza…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
We present a general-purpose interior-point solver for convex optimization problems with conic constraints. Our method is based on a homogeneous embedding method originally developed for general monotone complementarity problems and more…
This paper is concerned with solution algorithms for general convex vector optimization problems (CVOPs). So far, solution concepts and approximation algorithms for solving CVOPs exist only for bounded problems [Ararat et al. 2022, Doerfler…
We propose a novel adaptive, accelerated algorithm for the stochastic constrained convex optimization setting. Our method, which is inspired by the Mirror-Prox method, \emph{simultaneously} achieves the optimal rates for smooth/non-smooth…
It is possible to solve unbounded convex vector optimization problems (CVOPs) in two phases: (1) computing or approximating the recession cone of the upper image and (2) solving the equivalent bounded CVOP where the ordering cone is…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Convex optimization methods are employed to optimize a real-time (RT) system-on-chip (SoC) under a variety of physical resource-driven constraints, demonstrated on an industry MPEG2 encoder SoC. The power optimization is compared to…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
A convex envelope for the problem of finding the best approximation to a given matrix with a prescribed rank is constructed. This convex envelope allows the usage of traditional optimization techniques when additional constraints are added…
Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER,…
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…
Various R packages have been developed for the non-convex penalized estimation but they can only be applied to the smoothly clipped absolute deviation (SCAD) or minimax concave penalty (MCP). We develop an R package, entitled ncpen, for the…
Cooper is an open-source package for solving constrained optimization problems involving deep learning models. Cooper implements several Lagrangian-based first-order update schemes, making it easy to combine constrained optimization…
We introduce the R package ContaminatedMixt, conceived to disseminate the use of mixtures of multivariate contaminated normal distributions as a tool for robust clustering and classification under the common assumption of elliptically…
This paper proposes real-time sequential convex programming (RTSCP), a method for solving a sequence of nonlinear optimization problems depending on an online parameter. We provide a contraction estimate for the proposed method and, as a…
Cluster resource allocation is a multidimensional search problem that finds the best allocation of tasks to servers. Because the search space grows exponentially, modern approaches frame it as a mixed integer program (MIP) or a complex set…
In standard reinforcement learning (RL), a learning agent seeks to optimize the overall reward. However, many key aspects of a desired behavior are more naturally expressed as constraints. For instance, the designer may want to limit the…
We present a geometrical analysis on the completely positive programming reformulation of quadratic optimization problems and its extension to polynomial optimization problems with a class of geometrically defined nonconvex conic programs…
Convex approximation sets for multiobjective optimization problems are a well-studied relaxation of the common notion of approximation sets. Instead of approximating each image of a feasible solution by the image of some solution in the…
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective…