Related papers: Newton-type algorithms for inverse optimization I:…
Numerous multi-objective evolutionary algorithms have been designed for constrained optimisation over past two decades. The idea behind these algorithms is to transform constrained optimisation problems into multi-objective optimisation…
The imbalances and conditioning of the objective functions influence the performance of first-order methods for multiobjective optimization problems (MOPs). The latter is related to the metric selected in the direction-finding subproblems.…
We consider the problem of risk-sensitive control in a reinforcement learning (RL) framework. In particular, we aim to find a risk-optimal policy by maximizing the distortion riskmetric (DRM) of the discounted reward in a finite horizon…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction…
We consider optimal design of PDE-based Bayesian linear inverse problems with infinite-dimensional parameters. We focus on the A-optimal design criterion, defined as the average posterior variance and quantified by the trace of the…
We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…
Given a set of observations generated by an optimization process, the goal of inverse optimization is to determine likely parameters of that process. We cast inverse optimization as a form of deep learning. Our method, called deep inverse…
Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. The practical implementation of the gradient descent method to bilevel optimization encounters computational…
Many machine learning models depend on solving a large scale optimization problem. Recently, sub-sampled Newton methods have emerged to attract much attention for optimization due to their efficiency at each iteration, rectified a weakness…
Consider the problem of finding an optimal value of some objective functional subject to constraints over numerical domain. This type of problem arises frequently in practical engineering tasks. Nowdays almost all general methods for…
Second-order methods are of great importance for composite convex optimization problems due to their local super-linear convergence rates (under appropriate assumptions). However, the presence of even a simple nonsmooth function in the…
The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but…
Despite much research, hard weighted problems still resist super-polynomial improvements over their textbook solution. On the other hand, the unweighted versions of these problems have recently witnessed the sought-after speedups.…
The objective of this paper is to develop a duality between a novel Entropy Martingale Optimal Transport problem (A) and an associated optimization problem (B). In (A) we follow the approach taken in the Entropy Optimal Transport (EOT)…
We consider a class of constrained optimization problems with a possibly nonconvex non-Lipschitz objective and a convex feasible set being the intersection of a polyhedron and a possibly degenerate ellipsoid. Such problems have a wide range…
In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…
This paper presents a new fast and robust algorithm that provides fuel-optimal impulsive control input sequences that drive a linear time-variant system to a desired state at a specified time. This algorithm is applicable to a broad class…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
We study the following metric distortion problem: there are two finite sets of points, $V$ and $C$, that lie in the same metric space, and our goal is to choose a point in $C$ whose total distance from the points in $V$ is as small as…