We consider the problem of learning risk scores to prioritize individuals for scarce resources or interventions, from historical observational data affected by unobserved confounding. In settings such as public health and homelessness prevention, decisions about who receives a scarce resource (e.g., a hospital bed or housing) are often guided by a risk score assigned to … Read more
We propose a novel branch‑and‑bound algorithm that constructs rigorous outer approximations of the optimal point mapping for parametric optimization problems with guaranteed feasibility and optimality tolerances. The method uses the improvement‑function reformulation to define discarding and inclusion tests on sub-boxes, constructing a rigorous outer approximation. Under the same regularity conditions that ensure exactness of this … Read more
We revisit the framework of generalized Benders decomposition over a compact but non-finite master domain. We show by counterexample that strong general dual functions alone may fail to guarantee convergence. We then define a condition of uniform local strongness and prove that strong general dual functions satisfying this condition guarantee finite \(\epsilon\)-termination. Finally, we show … Read more
We present a Julia computational toolbox for linear optimization problems with joint affine chance constraints under elliptically symmetric uncertainty. The toolbox combines a spherical–radial oracle for estimating the joint probability and its gradient with three structured optimization methods: Proximal, Feasible, and Penalty. The oracle supports several elliptically symmetric distributions and is integrated with these methods … Read more
In this paper, we propose new adaptive proximal gradient algorithms to solve multiobjective optimization problems, where each objective function is the sum of a differentiable function and a proper, closed, convex function. Utilizing the local behavior of the differentiable terms we propose new adaptive ways to select stepsizes used in proximal gradient scheme. In particular, … Read more
Quantization-aware training (QAT) updates a full-precision shadow weight \(\mathbf{x}\) but deploys the quantized endpoint \(Q(\mathbf{x})\). Existing explanations for QAT largely view its success through the lens of shadow weights: QAT can move \(\mathbf{x}\) toward flatter basins, gain robustness from quantization-induced oscillations, or balance the shadow loss \(f(\mathbf{x})\) against the quantization error \(\|\mathbf{x}-Q(\mathbf{x})\|_2\). These perspectives do … Read more
Large police departments usually operate by assigning regular patrol units to pre-defined regions, with backup units covering multiple regions to handle periods of high demand or replace unavailable regular units. We develop a data-driven approach to determine the optimal number and deployment of these backup units across different shifts, minimizing the expected travel time to … Read more
State-of-the-art exact methods for the Maximum Cut problem are based on solving linear and semidefinite programming relaxations embedded into a branch-and-bound algorithm. For linear programming formulations, it was shown recently that it is thereby sufficient to enforce the integrality of the variables associated with the edges of a spanning tree. Our first contribution is to … Read more
Extending a classic result of Giannessi and Tomasin [\textit{Lecture Notes in Comput. Sci. 3}, Springer, 1973, pp. 437–449], this paper shows that a binary-constrained quadratic-defined optimization problem can be formulated as a binary-constrained linear program with linear complementarity constraints (Bi-LPCC). The term “quadratic-defined problems” encompasses many problems that are defined by quadratic functions in the … Read more
We give an exact algorithm for minimizing an arbitrary rational quadratic polynomial xTQx+ cTx+ γ over the integer points of a bounded rational polyhedron Ax ≤b. For n variables and m inequalities, the running time is 2O(n log(n+1))(m+ 1)O(n)φ_{A,Q}^O(n)(1 + φ)O(1), where φ_{A,Q} is one plus the maximum binary encoding length of an entry of … Read more