Related papers: Global Nonconvex Optimization with Integer Variabl…

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified…

The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their…

Point cloud alignment is a common problem in computer vision and robotics, with applications ranging from 3D object recognition to reconstruction. We propose a novel approach to the alignment problem that utilizes Bayesian nonparametrics to…

Achieving globally optimal point cloud registration under partial overlaps and large misalignments remains a fundamental challenge. While simultaneous transformation ($\boldsymbol{\theta}$) and correspondence ($\mathbf{P}$) estimation has…

In this paper, we propose an exact general algorithm for solving non-convex optimization problems, where the non-convexity arises due to the presence of an inverse S-shaped function. The proposed method involves iteratively approximating…

In exact sparse optimization problems on Rd (also known as sparsity constrained problems), one looks for solution that have few nonzero components. In this paper, we consider problems where sparsity is exactly measured either by the…

This paper deals with the problem of finding the globally optimal subset of h elements from a larger set of n elements in d space dimensions so as to minimize a quadratic criterion, with an special emphasis on applications to computing the…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

We introduce the idea that using optimal classification trees (OCTs) and optimal classification trees with-hyperplanes (OCT-Hs), interpretable machine learning algorithms developed by Bertsimas and Dunn [2017, 2018], we are able to obtain…

Optimal power flow (OPF) is an important problem in the operation of electric power systems. Due to the OPF problem's non-convexity, there may exist multiple local optima. Certifiably obtaining the global solution is important for certain…

This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…

In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…

In this paper, we propose the approximate Bregman proximal gradient algorithm (ABPG) for solving composite nonconvex optimization problems. ABPG employs a new distance that approximates the Bregman distance, making the subproblem of ABPG…

We present a technique for producing valid dual bounds for nonconvex quadratic optimization problems. The approach leverages an elegant piecewise linear approximation for univariate quadratic functions due to Yarotsky, formulating this…

Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…

Lately, a novel swarm intelligence model, namely the consensus-based optimization (CBO) algorithm, was introduced to deal with the global optimization problems. Limited by the conditions of Ito's formula, the convergence analysis of the…

We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…

For a nonlinear system (e.g. a robot) with its continuous state space trajectories constrained by a linear temporal logic specification, the synthesis of a low-level controller for mission execution often results in a non-convex…

In Part I of this paper, we proposed and analyzed a novel algorithmic framework for the minimization of a nonconvex (smooth) objective function, subject to nonconvex constraints, based on inner convex approximations. This Part II is devoted…

Non-linear least squares solvers are used across a broad range of offline and real-time model fitting problems. Most improvements of the basic Gauss-Newton algorithm tackle convergence guarantees or leverage the sparsity of the underlying…