Inverse optimization problems are bilevel optimization problems in which the leader modifies the follower’s objective such that a prescribed feasible solution becomes an optimal solution of the follower. They capture hierarchical decision-making problems like parameter estimation tasks or situations where a planner wants to steer an agent’s choice. In this work, we study integral inverse … Read more
This paper introduces a regularized, structure-exploiting Powell-Symmetric-Broyden (RSE-PSB) method under modified secant conditions for solving ill-posed inverse problems in both infinite dimensional and finite dimensional settings. The approximation of the symmetric, yet potentially indefinite, second-order term, which is neglected by standard Levenberg-Marquardt (LM) approaches, integrates regularization and structure exploitation directly within the Quasi-Newton (QN) framework, … Read more
Partial inverse combinatorial optimization problems are bilevel optimization problems in which the leader aims to incentivize the follower to include a given set of elements in the solution of their combinatorial problem. If the set of required elements defines a complete follower solution, the inverse combinatorial problem is solvable in polynomial time as soon as … Read more
This paper proposes a polynomial-time algorithm to construct the monotone stepwise curve that minimizes the sum of squared errors with respect to a given cloud of data points. The fitted curve is also constrained on the maximum number of steps it can be composed of and on the minimum step length. Our algorithm relies on … Read more
Inverse optimization is the problem of determining the values of missing input parameters that are closest to given estimates and that will make a given solution optimal. This study is concerned with the relationship of a particular inverse mixed integer linear optimization problem (MILPs) to both the original problem and the separation problem associated with … Read more
We investigate a class of moment problems, namely recovering a measure supported on the graph of a function from partial knowledge of its moments, as for instance in some problems of optimal transport or density estimation. We show that the sole knowledge of first degree moments of the function, namely linear measurements, is sufficient to … Read more
This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal solutions that correspond to different instances of the linear program. We introduce a new formulation of the problem that, … Read more
We study the problem of online learning (OL) from revealed preferences: a learner wishes to learn an agent’s private utility function through observing the agent’s utility-maximizing actions in a changing environment. We adopt an online inverse optimization setup, where the learner observes a stream of agent’s actions in an online fashion and the learning performance … Read more
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 optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision-making. In this paper, … Read more
In this paper we study a feasibility-seeking problem with percentage violation con- straints. These are additional constraints, that are appended to an existing family of constraints, which single out certain subsets of the existing constraints and declare that up to a speci ed fraction of the number of constraints in each subset is allowed to be … Read more