Related papers: Subdifferentials and Stability Analysis of Feasibl…
Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the…
In multiobjective optimisation, a set of scalable test problems with a variety of features allow researchers to investigate and evaluate the abilities of different optimisation algorithms, and thus can help them to design and develop more…
Polynomial and rational functions are the number one choice when it comes to modeling of radial distortion of lenses. However, several extrapolation and numerical issues may arise while using these functions that have not been covered by…
Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…
We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the…
This paper investigates stability properties of affine optimal control problems constrained by semilinear elliptic partial differential equations. This is done by studying the so called metric subregularity of the set-valued mapping…
We consider the stability of Robust Optimization problems with respect to perturbations in their uncertainty sets. We focus on Linear Optimization problems, including those with a possibly infinite number of constraints, also known as…
The fitting of physical models is often done only using a single target observable. However, when multiple targets are considered, the fitting procedure becomes cumbersome, there being no easy way to quantify the robustness of the model for…
Submodular functions allow to model many real-world optimisation problems. This paper introduces approaches for computing diverse sets of high quality solutions for submodular optimisation problems. We first present diversifying greedy…
The directional subdifferential of the value function gives an estimate on how much the optimal value changes under a perturbation in a certain direction. In this paper we derive upper estimates for the directional limiting and singular…
In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to…
In statistical inference, a discrepancy between the parameter-to-observable map that generates the data and the parameter-to-observable map that is used for inference can lead to misspecified likelihoods and thus to incorrect estimates. In…
Multi-objective optimization (MOO) is a prevalent challenge for Deep Learning, however, there exists no scalable MOO solution for truly deep neural networks. Prior work either demand optimizing a new network for every point on the Pareto…
We consider the problem of designing piecewise affine policies for two-stage adjustable robust linear optimization problems under right-hand side uncertainty. It is well known that a piecewise affine policy is optimal although the number of…
Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation of the Pareto front challenging. The present paper shows that certain algorithms…
Consider a problem where a set of feasible observations are provided by an expert and a cost function is defined that characterizes which of the observations dominate the others and are hence, preferred. Our goal is to find a set of linear…
We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an…
A vertex of a plane digraph is bimodal if all its incoming edges (and hence all its outgoing edges) are consecutive in the cyclic order around it. A plane digraph is bimodal if all its vertices are bimodal. Bimodality is at the heart of…
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimizers for a broad class of…
In Part 1 of this paper, we have estimated the Fr\'echet coderivative and the Mordukhovich coderivative of the stationary point set map of a smooth parametric optimization problem with one smooth functional constraint under total…