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Determining the vanishing points (VPs) in a Manhattan world, as a fundamental task in many 3D vision applications, consists of jointly inferring the line-VP association and locating each VP. Existing methods are, however, either sub-optimal…
The goal of this paper is to survey the properties of the eigenvalue relaxation for least squares binary problems. This relaxation is a convex program which is obtained as the Lagrangian dual of the original problem with an implicit compact…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
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…
When optimizing real-time systems, designers often face a challenging problem where the schedulability constraints are non-convex, non-continuous, or lack an analytical form to understand their properties. Although the optimization…
In this work, we present an algorithmically tractable safe approximation of distributionally robust optimization (DRO) problems that contain univariate indicator functions. The latter appear in different applications, but render the model…
We explore a multiple-stage variant of the min-max robust selection problem with budgeted uncertainty that includes queries. First, one queries a subset of items and gets the exact values of their uncertain parameters. Given this…
We use sensitivity analysis to design bounding-focused discretization (cutting-surface) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal bounding-focused discretization of…
We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. To decompose such problems we introduce the new concept of core points, i.e., integral points whose orbit polytopes are…
This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (CUP) for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis…
Subspace identification is a classical and very well studied problem in system identification. The problem was recently posed as a convex optimization problem via the nuclear norm relaxation. Inspired by robust PCA, we extend this framework…
We use a decision-theoretic framework to study the problem of forecasting discrete outcomes when the forecaster is unable to discriminate among a set of plausible forecast distributions because of partial identification or concerns about…
(Block-)coordinate minimization is an iterative optimization method which in every iteration finds a global minimum of the objective over a variable or a subset of variables, while keeping the remaining variables constant. While for some…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We consider box-constrained robust optimisation problems with implementation uncertainty. In this setting, the solution that a decision maker wants to implement may become perturbed. The aim is to find a solution that optimises the worst…