We prove an $\Omega(L/T)$ lower bound for the convergence rate of minimization in the class of functions that are convex and $L$-smooth relative to negative entropy on the standard $d$-simplex, valid for every first-order method when $d = \Omega(T^2)$. In particular, this shows that mirror descent is optimal up to a logarithmic factor in this … Read more
Parameter estimation is a fundamental challenge in the calibration of ordinary differential equation (ODE) models, where repeated numerical integration can lead to high computational cost. In this work, we investigate whether quantum algorithms can be leveraged to assist parameter estimation in nonlinear dynamical systems. We develop a hybrid classical–quantum framework that reformulates a data-assimilation-augmented parameter … Read more
Parameter estimation in nonlinear dynamical systems from observational data is a fundamental inverse problem with applications in many disciplines such as epidemiology, systems biology, climate science, and related fields. In practice, this is further complicated by the fact that observational data are often noisy, sparse, and available only for a subset of the state variables. … Read more
We study the computation of a second shortest simple \(s\)–\(t\) path (2-SP) in a directed graph with \(n\) nodes, \(m\) arcs and nonnegative integer arc costs bounded by \(C\). Working with reduced costs and a depth-first search that gives priority to a fixed shortest path \(P_{st}\), every candidate second path is a prefix of \(P_{st}\), … Read more
We study the Superiorization Methodology (SM) in the context of the General Dynamic String-Averaging (GDSA) method in the inconsistent case (that is, where the input operators don’t have a common fixed point) which primarily aims at achieving convex feasibility while simultaneously reducing an objective function. In many scientific and real-world problems modeled as constrained minimization … Read more
Very recently (2026), Bauschke and Tung extended from finite- to infinite-dimensional Hilbert spaces a result published by Meshulam in 1996 (following an earlier result of Aharoni-Duchet-Wajnryb from 1984) regarding the boundedness of infinite products of relaxed projections onto a finite family of closed affine subspaces. In the present note we extend in various ways the … Read more
The stable set problem admits various binary linear and quadratic formulations. The Shor relaxation of a particular quadratic formulation is the well-known theta body. We consider aggregations of quadratic constraints of this formulation, yielding exact and inexact quadratic formulations of the stable set problem, and then establish conditions under which the aggregated quadratic formulation is … Read more
We develop a symmetry-compatible framework for first-order methods on matrix optimization problems. The central principle is that the update rule for a matrix variable should be equivariant with respect to the natural symmetry group acting on that variable. For matrix representations of linear operators, this leads to bi-orthogonal equivariance under left and right orthogonal changes … Read more
Residential parcel lockers (RPLs), unlike their public counterparts, facilitate secure parcel delivery to occupants of private apartment and condominium buildings in urban areas. In this work, we consider the perspective of a last-mile parcel carrier that has access to an RPL in the lobby of a high-rise residential building. Motivated by growing e-commerce demand, we … Read more
Optimization models are built in a variety of modeling languages and solved by a variety of solvers, but once a solution exists, the information needed to understand it is fragmented: each solver exposes a partial, differently named set of native diagnostics, and the modeling language has already canonicalized the formulation the user wrote. We present … Read more