Related papers: KL-optimum designs: theoretical properties and pra…
For nonexpansive fixed-point problems, Halpern's method with optimal parameters, its so-called H-dual algorithm, and in fact, an infinite family of algorithms containing them, all exhibit the exactly minimax optimal convergence rates. In…
We study a class of nonconvex-nonconcave minimax problems in which the inner maximization problem satisfies a local Kurdyka-Lojasiewicz (KL) condition that may vary with the outer minimization variable. In contrast to the global KL or…
Distributed optimization algorithms are widely used in many industrial machine learning applications. However choosing the appropriate algorithm and cluster size is often difficult for users as the performance and convergence rate of…
This paper aims to develop an optimality theory for linear discriminant analysis in the high-dimensional setting. A data-driven and tuning free classification rule, which is based on an adaptive constrained $\ell_1$ minimization approach,…
Large language models (LLMs) have significant potential to improve operational efficiency in operations management. Deploying these models requires specifying a policy that governs response quality, shapes user experience, and influences…
Consider the problem of constructing an experimental design, optimal for estimating parameters of a given statistical model with respect to a chosen criterion. To address this problem, the literature usually provides a single solution.…
For linear time-invariant systems with uncertain parameters belonging to a finite set, we present a purely deterministic approach to multiple-model estimation and propose an algorithm based on the minimax criterion using constrained…
The experimental design for a generalized linear model (GLM) is important but challenging since the design criterion often depends on model specification including the link function, the linear predictor, and the unknown regression…
We address a broad class of optimization problems of finding quantum measurements, which includes the problems of finding an optimal measurement in the Bayes criterion and a measurement maximizing the average success probability with a…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
Minimizing the number of patients exposed to potentially harmful drugs in early onco logical trials is a major concern during planning. Adaptive designs account for the inherent uncertainty about the true effect size by determining the…
A central goal in designing clinical trials is to find the test that maximizes power (or equivalently minimizes required sample size) for finding a false null hypothesis subject to the constraint of type I error. When there is more than one…
The past century has seen a steady increase in the need of estimating and predicting complex systems and making (possibly critical) decisions with limited information. Although computers have made possible the numerical evaluation of…
We investigate R-optimal designs for multi-response regression models with multi-factors, where the random errors in these models are correlated. Several theoretical results are derived for Roptimal designs, including scale invariance,…
This paper is devoted to establishing an enhanced Fritz John type first-order necessary condition for a general constrained nonlinear infinite-dimensional optimization problem. Unlike traditional constraint qualifications in optimization…
We investigate numerically the optimal constants in Lieb-Thirring inequalities by studying the associated maximization problem. We use a monotonic fixed-point algorithm and a finite element discretization to obtain trial potentials which…
We examine the problem of optimal design in the context of filtering multiple random walks. Specifically, we define the steady state E-optimal design criterion and show that the underlying optimization problem leads to a second order cone…
The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…
Optimal transport is a geometrically intuitive, robust and flexible metric for sample comparison in data analysis and machine learning. Its formal Riemannian structure allows for a local linearization via a tangent space approximation. This…
Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in…