Related papers: A unified framework for solving a general class of…
Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic…
Generalized moment problems optimize functional expectation over a class of distributions with generalized moment constraints, i.e., the function in the moment can be any measurable function. These problems have recently attracted growing…
Optimization of frame structures is formulated as a~non-convex optimization problem, which is currently solved to local optimality. In this contribution, we investigate four optimization approaches: (i) general non-linear optimization, (ii)…
Global optimization of decision trees is a long-standing challenge in combinatorial optimization, yet such models play an important role in interpretable machine learning. Although the problem has been investigated for several decades, only…
This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator…
This paper presents a weighted optimization framework that unifies the binary,multi-valued, continuous, as well as mixture of discrete and continuous treatment, under the unconfounded treatment assignment. With a general loss function, the…
Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_y$) on $R^n$ whose description depends on the parameter $y\inY$. We assume that one can compute all moments of some probability measure $\phi$ on…
This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
Consider the setting of constrained optimization, with some parameters unknown at solving time and requiring prediction from relevant features. Predict+Optimize is a recent framework for end-to-end training supervised learning models for…
This work proposes a framework for multistage adjustable robust optimization that unifies the treatment of three different types of endogenous uncertainty, where decisions, respectively, (i) alter the uncertainty set, (ii) affect the…
We describe a framework for reformulating and solving optimization problems that generalizes the well-known framework originally introduced by Benders. We discuss details of the application of the procedures to several classes of…
Performative prediction characterizes environments where predictive models alter the very data distributions they aim to forecast, triggering complex feedback loops. While prior research treats single-agent and multi-agent performativity as…
In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…
A new relaxed variant of interior point method for low-rank semidefinite programming problems is proposed in this paper. The method is a step outside of the usual interior point framework. In anticipation to converging to a low-rank primal…
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical…
In this paper we develop a unified approach for solving a wide class of sequential selection problems. This class includes, but is not limited to, selection problems with no-information, rank-dependent rewards, and considers both fixed as…
We propose a new approach to solving bilevel optimization problems, intermediate between solving full-system optimality conditions with a Newton-type approach, and treating the inner problem as an implicit function. The overall idea is to…
This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…