A new algorithm for smooth constrained optimization is proposed that never computes the value of the problem’s objective function and that handles both equality and inequality constraints. The algorithm uses an adaptive switching strategy between a normal step aiming at reducing constraint’s infeasibility and a tangential step improving dual optimality, the latter being inspired by … Read more
We describe inexact proximal Newton-like methods for solving degenerate regularized optimization problems and for the broader problem of finding a zero of a generalized equation that is the sum of a continuous map and a maximal monotone operator. Superlinear convergence for both the distance to the solution set and a certain measure of first-order optimality … Read more
Outer-approximation-based branch-and-bound is a common algorithmic framework for solving MINLPs (mixed-integer nonlinear programs) to global optimality, with branching variable selection critically influencing overall performance. In modern global MINLP solvers, it is unclear whether branching on fractional integer variables should be prioritized over spatial branching on variables, potentially continuous, that show constraint violations, with different solvers … Read more
In model extraction attacks, the goal is to reveal the parameters of a black-box machine learning model by querying the model for a selected set of data points. Due to an increasing demand for explanations, this may involve counterfactual queries besides the typically considered factual queries. In this work, we consider linear models and three … Read more
Bilevel optimization is a powerful tool for modeling hierarchical decision-making processes, which arise in various real-world applications. Due to their nested structure, however, bilevel problems are intrinsically hard to solve—even if all variables are continuous and all parameters of the problem are exactly known. Further challenges arise if mixed-integer aspects and problems under uncertainty are … Read more
Public school bus routes can change from year to year as students and their home locations change. However, school administrators benefit from the ability to predict future transportation needs on multi-year time scales. With this motivation in mind, this paper develops planning models for school bus routing when student locations are not known with certainty. … Read more
ArticleDownload View PDF
We study the Rectified Linear Unit (ReLU) dual, an existing dual formulation for stochastic programs that reformulates non-anticipativity constraints using ReLU functions to generate tight, non-convex, and mixed-integer representable cuts. While this dual reformulation guarantees convergence with mixed-integer state variables, it admits multiple optimal solutions that can yield weak cuts. To address this issue, we … Read more
We present a brief structural equivalence between the symmetric TSP and a constrained Group Steiner Tree Problem (cGSTP) defined on a simplicial incidence graph. Given the complete weighted graph on the city set V, we form the bipartite incidence graph between triangles and edges. Selecting an admissible, disk-like set of triangles induces a unique boundary … Read more
We propose an Adagrad-like algorithm for multi-objective unconstrained optimization that relies on the computation of a common descent direction only. Unlike classical local algorithms for multi-objective optimization, our approach does not rely on the dominance property to accept new iterates, which allows for a flexible and function-free optimization framework. New points are obtained using an … Read more