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We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
In multi-objective optimization, several potentially conflicting objective functions need to be optimized. Instead of one optimal solution, we look for the set of so called non-dominated solutions. An important subset is the set of…
In this short note, we discuss a goal-oriented multiobjective optimization problem for system performance assessment. The objective function for such optimization problem, which is usually a composite of different performance indices…
In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems considering subsets of the objective functions. If the…
Optimizing the performance of many objectives (instantiated by tasks or clients) jointly with a few Pareto stationary solutions (models) is critical in machine learning. However, previous multi-objective optimization methods often focus on…
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…
In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…
Many real-world decision-making problems involve optimizing multiple objectives simultaneously, rendering the selection of the most preferred solution a non-trivial problem: All Pareto optimal solutions are viable candidates, and it is…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
Most real optimization problems are defined over a mixed search space where the variables are both discrete and continuous. In engineering applications, the objective function is typically calculated with a numerically costly black-box…
We consider the problem of black-box multi-objective optimization (MOO) using expensive function evaluations (also referred to as experiments), where the goal is to approximate the true Pareto set of solutions by minimizing the total…
Multiobjective combinatorial optimization (MOCO) problems can be found in many real-world applications. However, exactly solving these problems would be very challenging, particularly when they are NP-hard. Many handcrafted heuristic…
Interior point methods for solving linearly constrained convex programming involve a variable projection matrix at each iteration to deal with the linear constraints. This matrix often becomes ill-conditioned near the boundary of the…
We consider the optimization of an uncertain objective over continuous and multi-dimensional decision spaces in problems in which we are only provided with observational data. We propose a novel algorithmic framework that is tractable,…
The article presents a study on the biobjective inventory routing problem. Contrary to most previous research, the problem is treated as a true multi-objective optimization problem, with the goal of identifying Pareto-optimal solutions. Due…
In this study, we consider the subset selection problems with submodular or monotone discrete objective functions under partition matroid constraints where the thresholds are dynamic. We focus on POMC, a simple Pareto optimization approach…
We study the oracle complexity of finding $\varepsilon$-Pareto stationary points in smooth multiobjective optimization with $m$ objectives. Progress is measured by the Pareto stationarity gap $\mathcal{G}(x)$, the norm of the best convex…
To date, the multi-objective optimization literature has mainly focused on conflicting objectives, studying the Pareto front, or requiring users to balance tradeoffs. Yet, in machine learning practice, there are many scenarios where such…
Inverse optimization, determining parameters of an optimization problem that render a given solution optimal, has received increasing attention in recent years. While significant inverse optimization literature exists for convex…