Related papers: Non-Linear Counterfactual Aggregate Optimization
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Submodular function minimization is well studied, and existing algorithms solve it exactly or up to arbitrary accuracy. However, in many applications, such as structured sparse learning or batch Bayesian optimization, the objective function…
Non-linear performance measures are widely used for the evaluation of learning algorithms. For example, $F$-measure is a commonly used performance measure for classification problems in machine learning and information retrieval community.…
Nonlinear regression has been extensively employed in many computer vision problems (e.g., crowd counting, age estimation, affective computing). Under the umbrella of deep learning, two common solutions exist i) transforming nonlinear…
Sub-sampling is a common and often effective method to deal with the computational challenges of large datasets. However, for most statistical models, there is no well-motivated approach for drawing a non-uniform subsample. We show that the…
We consider nonlinear, or "event-dependent", sampling, i.e. such that the sampling instances {tk} depend on the function being sampled. The use of such sampling in the construction of Lebesgue's integral sums is noted and discussed as…
Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical…
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…
In this paper, we study the decentralized optimization problem of minimizing a finite sum of continuously differentiable and possibly nonconvex functions over a fixed-connected undirected network. We propose a unified decentralized…
In this paper, a new one-parameter filled function approach is developed for nonlinear multi-objective optimization. Inspired by key filled function ideas from single-objective optimization, the proposed method is adapted to the…
An algorithm capable of finding a likely global optimum (minimum) and a set of sub-optimal points for arbitrary generic functions of several variables is presented. The algorithm is designed to deal even with functions of complex behavior,…
A novel neural network (NN) approach is proposed for constrained optimization. The proposed method uses a specially designed NN architecture and training/optimization procedure called Neural Optimization Machine (NOM). The objective…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
In practice, most of the optimization problems are non-linear requiring certain interactive solutions and approaches to model. In 5G Advanced and Beyond network slicing, mathematically modeling the users, type of service distributions and…
We analyze the performance of alternating minimization for loss functions optimized over two variables, where each variable may be restricted to lie in some potentially nonconvex constraint set. This type of setting arises naturally in…
In this article, we present a problem of nonlinear constraint optimization with equality and inequality constraints. Objective functions are defined to be nonlinear and optimizers may have a lower and upper bound. We solve the optimization…
The nonlinear conjugate gradient methods are known to be an effective approach for standard unconstrained optimization problems especially for large-scale problems. This paper proposes a proximal nonlinear conjugate gradient method, which…
Distributed optimization algorithms have been studied extensively in the literature; however, underlying most algorithms is a linear consensus scheme, i.e. averaging variables from neighbors via doubly stochastic matrices. We consider…