Related papers: A note on solving nonlinear optimization problems …
Trust-region (TR) and adaptive regularization using cubics (ARC) have proven to have some very appealing theoretical properties for non-convex optimization by concurrently computing function value, gradient, and Hessian matrix to obtain the…
Many complex multi-target prediction problems that concern large target spaces are characterised by a need for efficient prediction strategies that avoid the computation of predictions for all targets explicitly. Examples of such problems…
Most existing work uses dual decomposition and subgradient methods to solve Network Utility Maximization (NUM) problems in a distributed manner, which suffer from slow rate of convergence properties. This work develops an alternative…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
We consider the problem of using experimental time-series data for parameter estimation in nonlinear ordinary differential equations, focusing on the case where the data is noisy, sparse, irregularly sampled, includes multiple experiments,…
Traditional optimization methods rely on the use of single-precision floating point arithmetic, which can be costly in terms of memory size and computing power. However, mixed precision optimization techniques leverage the use of both…
Due to the substantial computational cost, training state-of-the-art deep neural networks for large-scale datasets often requires distributed training using multiple computation workers. However, by nature, workers need to frequently…
Probabilistic circuits (PCs) offer a promising avenue to perform embedded reasoning under uncertainty. They support efficient and exact computation of various probabilistic inference tasks by design. Hence, hardware-efficient computation of…
We introduce a particular optimization problem that minimizes the sum of a non-convex quadratic function and logarithmic barrier-functions in a $\ell_\infty$-trust-region (i.e. cube). Our paper covers three topics. We explain the relevance…
Iterative optimization algorithms depend on access to information about the objective function. In a differentiable programming framework, this information, such as gradients, can be automatically derived from the computational graph. We…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
This paper describes the optimisation theory on which VPFIT, a non-linear least-squares program for modelling absorption spectra, is based. Particular attention is paid to precision. Voigt function derivatives have previously been…
In recent advances in solving the problem of transmission network expansion planning, the use of robust optimization techniques has been put forward, as an alternative to stochastic mathematical programming methods, to make the problem…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
A stochastic-gradient-based interior-point algorithm for minimizing a continuously differentiable objective function (that may be nonconvex) subject to bound constraints is presented, analyzed, and demonstrated through experimental results.…
In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then,…
Spatial processes observed in various fields, such as climate and environmental science, often occur on a large scale and demonstrate spatial nonstationarity. Fitting a Gaussian process with a nonstationary Mat\'ern covariance is…
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
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…