We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based methods asymptotically. In contrast with previous literature, where convergence is established based on worst-case analysis, our framework provides a strong convergence guarantee … Read more
Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for multiobjective optimization converge slowly, even for well-conditioned problems, due to the objective imbalances. To address this limitation, we incorporate curvature information to scale each objective within … Read more
We consider a two-player Nash game in which each player represents a fleet of unmanned aerial vehicles. Each fleet is supposed to distribute information among fleet members, while simultaneously trying to prevent the opposite fleet from achieving this. Using the electro-magnetic spectrum’s properties, we model each fleet’s task as a nonlinear Nash game. By reformulating … Read more
This paper develops a parameter-free adaptive proximal bundle method with two important features: 1) adaptive choice of variable prox stepsizes that “closely fits” the instance under consideration; and 2) adaptive criterion for making the occurrence of serious steps easier. Computational experiments show that our method performs substantially fewer consecutive null steps (i.e., a shorter cycle) … Read more
\(\) We consider the theoretical computational complexity of finding locally optimal solutions to bilevel linear optimization problems (BLPs), from the leader’s perspective. We show that, for any constant \(c > 0\), the problem of finding a leader’s solution that is within Euclidean distance \(c^n\) of any locally optimal leader’s solution, where \(n\) is the total … Read more
We present column elimination as a general framework for solving (large-scale) integer programming problems. In this framework, solutions are represented compactly as paths in a directed acyclic graph. Column elimination starts with a relaxed representation, that may contain infeasible paths, and solves a constrained network flow over the graph to find a solution. It then … Read more
Multiobjective optimization is widely used in applications for modeling and solving complex decision-making problems. To help resolve computational and cognitive difficulties associated with problems which have more than 3 or 4 objectives, we propose a decomposition and coordination methodology to support decision making for large multiobjective optimization problems (MOPs) with global, quasi-global, and local variables. … Read more
\(\) Bilevel optimization has recently attracted considerable attention due to its abundant applications in machine learning problems. However, existing methods rely on prior knowledge of problem parameters to determine stepsizes, resulting in significant effort in tuning stepsizes when these parameters are unknown. In this paper, we propose two novel tuning-free algorithms, D-TFBO and S-TFBO. D-TFBO … Read more
This tutorial provides an introduction to the use of decision diagrams for solving discrete optimization problems. A decision diagram is a graphical representation of the solution space, representing decisions sequentially as paths from a root node to a target node. By merging isomorphic subgraphs (or equivalent subproblems), decision diagrams can compactly represent an exponential solution … Read more
We present an algorithm for triobjective nonlinear integer programs that combines the epsilon-constrained method with available oracles for biobjective integer programs. We prove that our method is able to detect the nondominated set within a finite number of iterations. Specific strategies to avoid the detection of weakly nondominated points are devised. The method is then … Read more