Mixed integer nonlinear programs with binary coupling decisions naturally model selective coordination tasks where a fixed penalty is incurred whenever adjacent continuous variables differ. A prominent example is the classical Potts model, which is widely used in statistical inference. However, exact solvability remains theoretically challenging since the problem is NP hard on general graphs, and … Read more
Feature-based newsvendor models use observable covariates to tailor inventory decisions, aiming to balance holding and shortage costs under demand uncertainty. However, high-dimensional feature sets often hinder interpretability and inflate data collection and implementation costs. This paper studies variable selection for the feature-based newsvendor problem under a hard cardinality constraint on the number of selected features. … Read more
Georeferenced synthetic populations are essential inputs for agent-based simulations in epidemiology, transportation, and urban planning, yet existing methods for spatial allocation of households to residences lack formal optimality guarantees. We present a two-stage mathematical framework for generating such populations from publicly available census data. The first stage combines Iterative Proportional Fitting (IPF) with a mixed-integer … Read more
This paper studies the Sinkhorn distributionally robust hypothesis testing (SDRHT) problem, seeking a robust detector against least-favorable distributions in Sinkhorn discrepancy-based ambiguity sets centered at the empirical distributions. Existing approaches solve this problem by solving large-scale conic programs, which are not scalable. To overcome this, we propose a generative framework that learns least-favorable distributions and … Read more
For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher’s augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this paper, the analysis of this algorithm is extended, offering a two-fold contribution. First, it is shown that … Read more
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
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
Azuma, Kim, and Yamashita formulated the verification problem for one-layer ReLU networks as a quadratically constrained quadratic program and established tight semidefinite relaxations for the edgeless case and for one-unit settings. In this work, we represent the sharing pattern of undecided ReLUs over a box input set through an input-sharing graph and focus on the … Read more
Our project investigates replacing the classical adversarial discriminator in GAN training with a kernel-based distance metric, namely Kernel Stein Discrepancy (KSD). We assess whether a kernelized objective can improve training stability and efficiency without compromising sample quality, and we evaluate accelerated Nystrom approximations with Renyi landmark selection on CIFAR-10. ArticleDownload View PDF
A new Block Coordinate Gradient (BCG) method, dubbed bAdag, for smooth, nonconvex minimization problem is proposed; it falls in the class of Objective Function Free Optimization (OFFO) methods, and it is based on the AdaGrad algorithm. At each iteration, our method computes an adaptive step size based on the cumulative sum of block gradients, instead … Read more