Related papers: Nonlinear Optimization in R using nlopt

We systematically explore a class of constrained optimization problems with linear objective function and constraints that are linear combinations of logarithms of the optimization variables. Such problems can be viewed as a generalization…

Domain reduction techniques are at the core of any global optimization solver for NLP or MINLP problems. In this paper, we delve into several of these techniques and assess the impact they may have in the performance of an RLT-based…

We consider a popular family of constrained optimization problems arising in machine learning that involve optimizing a non-decomposable evaluation metric with a certain thresholded form, while constraining another metric of interest.…

Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…

Study about theory and algorithms for constrained optimization usually assumes that the feasible region of the optimization problem is nonempty. However, there are many important practical optimization problems whose feasible regions are…

A new pattern search method for bound constrained optimization is introduced. The proposed algorithm employs the coordinate directions, in a suitable way, with a nonmonotone line search for accepting the new iterate, without using…

Nonlinear metrics, such as the F1-score, Matthews correlation coefficient, and Fowlkes-Mallows index, are often used to evaluate the performance of machine learning models, in particular, when facing imbalanced datasets that contain more…

In this paper, we study a class of approximation problems, appearing in data approximation and signal processing. The approximations are constructed as combinations of polynomial splines (piecewise polynomials), whose parameters are subject…

In this note we develop a linear programming framework to produce upper and lower bounds for the lonely runner problem.

This paper proposes a new robust optimization (RO) formulation namely the RO under objective functional uncertainty (ObRO). The ObRO adopts a min-max structure where the inner problem finds the worst-case objective function in a continuous…

In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…

We consider a class of optimization problems that involve determining the maximum value that a function in a particular class can attain subject to a collection of difference constraints. We show that a particular linear programming…

While the theory of operator approximation with any given accuracy is well elaborated, the theory of {best constrained} constructive operator approximation is still not so well developed. Despite increasing demands from applications this…

We study the optimal approximation of the solution of an operator equation by certain n-term approximations with respect to specific classes of frames. We study worst case errors and the optimal order of convergence and define suitable…

This paper explores a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraints are known. We allow the objective and constraint function to…

We are interested in ensemble methods to solve multi-objective optimization problems. An ensemble Kalman method is proposed to solve a formulation of the nonlinear problem using a weighted function approach. An analysis of the mean field…

We study a class of convex-concave min-max problems in which the coupled component of the objective is linear in at least one of the two decision vectors. We identify such problem structure as interpolating between the bilinearly and…

In this work, we consider an optimal control problem subject to a nonlinear PDE constraint and apply it to the regularized $p$-Laplace equation. To this end, a reduced unconstrained optimization problem in terms of the control variable is…

Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…

The problem of minimizing a separable convex function under linearly coupled constraints arises from various application domains such as economic systems, distributed control, and network flow. The main challenge for solving this problem is…