Can gradient descent be accelerated by just choosing better stepsizes? Surprisingly, the answer is yes. This short expository article provides an accessible introduction to this phenomenon of stepsize hedging. ArticleDownload View PDF
We introduce a sequential version of the minimum $s$-$t$ cut problem, defined by a directed graph with source $s$ and sink $t$, and nonnegative random variables for each arc representing arc weights. We start with a working set $S = \{s\}$ and observe weight realizations for outgoing arcs from $S$ only. We choose to either … Read more
Lagrangian relaxation is a well-established technique for deriving strong bounds in single-objective discrete optimization. Its generalization to the multiobjective setting is not straightforward, as preserving the multiobjective structure leads to bound sets rather than scalar bounds. Recent studies show the existence of Lagrange multipliers that can yield tighter bound sets than those obtained from convex … Read more
This paper resolves an open problem posed in the literature by proving that, in dual-sourcing inventory systems, the optimality gap of tailored base-surge (TBS) policies decays exponentially with the regular source lead time, with the express-source lead time fixed. In contrast to the existing approach, which relies on conditional Jensen inequalities and a vanishing-discount argument … Read more
Multi-objective optimization is central to many engineering and machine learning applications, where multiple objectives must be optimized in balance. While multi-gradient based optimization methods combine these objectives in each step, such methods require computing gradients with respect to all variables at every iteration, resulting in high computational costs in large-scale settings. In this work, we … Read more
We propose an exact binary search-based branch-and-bound algorithm, termed the Quadtree Search Method, for solving bi-objective integer programs. The existing literature on criterion space search methods for multi-objective optimization predominantly assumes that subproblems can be solved to optimality, an assumption that becomes computationally prohibitive for hard instances. In contrast, our approach departs from this assumption … Read more
In this study, we model the supervised feature selection problem using a novel approach: convex bi-objective optimization. Traditional methods have addressed this problem by maximizing relevance to class labels and minimizing redundancy among features. Recently, Wang et al. [30] formulated this problem as a single-objective convex optimization, yielding only a unique solution. Unlike that, we … Read more
The paper presents a three-phase algorithm to compute the set of nondominated points for the binary version of the uncapacitated facility location problem with two objectives. The first phase constructs a paving in objective space which is a collection of boxes that covers all nondominated points. The paving procedure is a branch and bound algorithm … Read more
This paper addresses the challenge of enhancing public policy decision-making by efficiently solving principal-agent models (PAMs) for public-private partnerships, a critical yet computationally demanding problem. We develop a fast, interpretable, and generalizable approach to support policy decisions under these settings. We propose an interpretable ensemble heuristic (EH) that integrates Machine Learning (ML), Operations Research (OR), … Read more
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and formalize it using Lie group theory. Fixing a Lie group action on the outcome space and a reference distribution, we study optimal transport … Read more