Related papers: Nonlinear Optimization in R using nlopt
An adaptive regularization algorithm for unconstrained nonconvex optimization is proposed that is capable of handling inexact objective-function and derivative values, and also of providing approximate minimizer of arbitrary order. In…
The paper develops an optimal regulator for a general class of multi-input affine nonlinear systems minimizing a nonlinear cost functional with infinite horizon. The cost functional is general enough to enforce saturation limits on the…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defined by the $ \ell_0 $-quasi-norm. This term is used to obtain…
This paper presents a novel outer approximation algorithm for nonsmooth mixed-integer nonlinear programming (MINLP) problems. The method proceeds by fixing the integer variables and solving the resulting nonlinear convex subproblem. When…
In this paper, we focus on nonlinear infinite-norm minimization problems that have many applications, especially in computer science and operations research. We set a reliable Lagrangian dual aproach for solving this kind of problems in…
Shor's r-algorithm (Shor, Zhurbenko (1971), Shor (1979)) with space stretching in the direction of difference of two adjacent subgradients is a competitive method of nonsmooth optimization. However, the original r-algorithm is designed to…
This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local…
We consider the minimization of submodular functions subject to ordering constraints. We show that this optimization problem can be cast as a convex optimization problem on a space of uni-dimensional measures, with ordering constraints…
This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of such problems, reducing it in particular to a fixed point argument in R. Errors estimates and numerical experiments…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
We present a novel method for mixed-integer optimization problems with multivariate and Lipschitz continuous nonlinearities. In particular, we do not assume that the nonlinear constraints are explicitly given but that we can only evaluate…
The open-source nonlinear solver Ipopt (https://projects.coin-or.org/Ipopt) is a widely-used software package for the solution of large-scale non-linear optimization problems. At its heart, it employs a third-party linear solver to solve a…
Trajectory optimization is a powerful tool for robot motion planning and control. State-of-the-art general-purpose nonlinear programming solvers are versatile, handle constraints effectively and provide a high numerical robustness, but they…
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial…
We study the problem of policy optimization (PO) with linear temporal logic (LTL) constraints. The language of LTL allows flexible description of tasks that may be unnatural to encode as a scalar cost function. We consider LTL-constrained…
In some optimal control problems, complex relationships between states and inputs cannot be easily represented using continuous constraints, necessitating the use of discrete logic instead. This paper presents a method for incorporating…
Quantifying extra functions, herein referred to as outcome functions, over optimal solutions of an optimization problem can provide decision makers with additional information on a system. This bears more importance when the optimization…
In this paper we focus on the solution of online problems with time-varying, linear equality and inequality constraints. Our approach is to design a novel online algorithm by leveraging the tools of control theory. In particular, for the…