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A novel decomposition scheme to solve parametric non-convex programs as they arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of a fixed number of alternating proximal gradient steps and a dual update per time…
In this work, we develop an adaptive, multivariate partitioning algorithm for solving mixed-integer nonlinear programs (MINLP) with multi-linear terms to global optimality. This iterative algorithm primarily exploits the advantages of…
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…
In this paper, we consider the tensor eigenvalue complementarity problem which is closely related to the optimality conditions for polynomial optimization, as well as a class of differential inclusions with nonconvex processes. By…
Matrix factorization is a popular approach for large-scale matrix completion. The optimization formulation based on matrix factorization can be solved very efficiently by standard algorithms in practice. However, due to the non-convexity…
In this paper we propose a new method to stabilise non-symmetric indefinite problems. The idea is to solve a forward and an adjoint problem simultaneously using a suitable stabilised finite element method. Both stabilisation of the element…
Given $n$ points in a $d$ dimensional Euclidean space, the Minimum Enclosing Ball (MEB) problem is to find the ball with the smallest radius which contains all $n$ points. We give a $O(nd\Qcal/\sqrt{\epsilon})$ approximation algorithm for…
We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbb{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to…
In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…
In nonlinear elasticity, finding the deformation of a material which minimizes a given stored energy density is a challenging calculus of variations problem which may fail to have minimizers: the energy optimal material forms infinitely…
In this paper, we propose an inexact block coordinate descent algorithm for large-scale nonsmooth nonconvex optimization problems. At each iteration, a particular block variable is selected and updated by inexactly solving the original…
Low-rank tensor completion problem aims to recover a tensor from limited observations, which has many real-world applications. Due to the easy optimization, the convex overlapping nuclear norm has been popularly used for tensor completion.…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
The low-rank tensor completion (LRTC) problem aims to reconstruct a tensor from partial sample information, which has attracted significant interest in a wide range of practical applications such as image processing and computer vision.…
This paper proposes a general fixture layout design framework that directly integrates the system equation with the convex relaxation method. Note that the optimal fixture design problem is a large-scale combinatorial optimization problem,…
We address a large-scale and nonconvex optimization problem, involving an aggregative term. This term can be interpreted as the sum of the contributions of N agents to some common good, with N large. We investigate a relaxation of this…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
We consider solving high-order semidefinite programming (SDP) relaxations of nonconvex polynomial optimization problems (POPs) that often admit degenerate rank-one optimal solutions. Instead of solving the SDP alone, we propose a new…
We develop recursive, data-driven, stochastic subgradient methods for optimizing a new, versatile, and application-driven class of convex risk measures, termed here as mean-semideviations, strictly generalizing the well-known and popular…