Related papers: Gaining or losing perspective
In this paper, we study two classes of optimal reinsurance models from perspectives of both insurers and reinsurers by minimizing their convex combination where the risk is measured by a distortion risk measure and the premium is given by a…
In this work, we investigate an efficient numerical approach for solving higher order statistical methods for blind and semi-blind signal recovery from non-ideal channels. We develop numerical algorithms based on convex optimization…
Gas transportation and storage has become one of the most relevant and important optimization problems in energy systems. This problem inherently includes highly nonlinear and nonconvex aspects due to gas physics, and discrete aspects due…
Inverse optimization (IO) aims to determine optimization model parameters from observed decisions. However, IO is not part of a data scientist's toolkit in practice, especially as many general-purpose machine learning packages are widely…
This paper introduces mixed-integer optimization methods to solve regression problems that incorporate fairness metrics. We propose an exact formulation for training fair regression models. To tackle this computationally hard problem, we…
We derive a closed form description of the convex hull of mixed-integer bilinear covering set with bounds on the integer variables. This convex hull description is determined by considering some orthogonal disjunctive sets defined in a…
The pooling problem has applications, e.g., in petrochemical refining, water networks, and supply chains and is widely studied in global optimization. To date, it has largely been treated deterministically, neglecting the influence of…
In the paper, we develop a composite version of Mirror Prox algorithm for solving convex-concave saddle point problems and monotone variational inequalities of special structure, allowing to cover saddle point/variational analogies of what…
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
In this paper, we consider a class of structured nonsmooth fractional minimization, where the first part of the objective is the ratio of a nonnegative nonsmooth nonconvex function to a nonnegative nonsmooth convex function, while the…
We consider quadratic optimization in variables $(x,y)$ where $0\le x\le y$, and $y\in\{0,1\}^n$. Such binary $y$ are commonly refered to as "indicator" or "switching" variables and occur commonly in applications. One approach to such…
This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization techniques and mixed-integer linear programming, robust optimization,…
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
In the context of structured nonconvex optimization, we estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal problem. The estimates rely on detailed…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
We give necessary and sufficient conditions for minimality of generalized minimizers for linear-growth functionals of the form \[ \mathcal F[u] := \int_\Omega f(x,u(x)) \, \text{d}x, \qquad u:\Omega \subset \mathbb R^N\to \mathbb R^d, \]…
Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. This work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear…
In this paper, we consider two paradigms that are developed to account for uncertainty in optimization models: robust optimization (RO) and joint estimation-optimization (JEO). We examine recent developments on efficient and scalable…
We investigate the theoretical complexity of branch-and-bound (BB) and cutting plane (CP) algorithms for mixed-integer optimization. In particular, we study the relative efficiency of BB and CP, when both are based on the same family of…
Using machine learning to solve combinatorial optimization (CO) problems is challenging, especially when the data is unlabeled. This work proposes an unsupervised learning framework for CO problems. Our framework follows a standard…