Related papers: On the implementation of a global optimization met…
Mathematical optimization is a fundamental tool for decision-making in a wide range of applications. However, in many real-world scenarios, the parameters of the optimization problem are not known a priori and must be predicted from…
This article presents the first mixed-integer linear programming (MILP)-based iterative algorithm to solve factorable mixed-integer nonlinear programs (MINLPs) with bounded, differentiable periodic functions to global optimality with an…
Geometric programming is an important class of optimization problems that enable practitioners to model a large variety of real-world applications, mostly in the field of engineering design. In many real life optimization problem…
Multivariate adaptive regression splines (MARS) is a flexible statistical modeling method that has been popular for data mining applications. MARS has also been employed to approxmiate unknown relationships in optimzation for complex…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
In this paper we consider multi-objective optimization problems over a box. The problem is very relevant and several computational approaches have been proposed in the literature. They broadly fall into two main classes: evolutionary…
This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…
In this paper, a new localized radial basis function (RBF) method based on partition of unity (PU) is proposed for solving boundary and initial-boundary value problems. The new method is benefited from a direct discretization approach and…
(Renegar, 2016) introduced a novel approach to transforming generic conic optimization problems into unconstrained, uniformly Lipschitz continuous minimization. We introduce {\it radial transformations} generalizing these ideas, equipped…
Reduced density matrix functional theory (RDMFT) calculations are usually implemented in a decoupled manner, where the orbital and occupation optimizations are repeated alternately. Typically, orbital updates are performed using the unitary…
We consider interpolation-based derivative-free optimization in settings where only some derivatives are available. Such situations arise naturally in scientific computing applications involving simulations, adjoint-enabled components,…
Decentralized optimization is widely used in large scale and privacy preserving machine learning and various distributed control and sensing systems. It is assumed that every agent in the network possesses a local objective function, and…
This paper deals with two kinds of the one-dimensional global optimization problems over a closed finite interval: (i) the objective function $f(x)$ satisfies the Lipschitz condition with a constant $L$; (ii) the first derivative of $f(x)$…
Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee…
In machine learning, nonconvex optimization problems with multiple local optimums are often encountered. Graduated Optimization Algorithm (GOA) is a popular heuristic method to obtain global optimums of nonconvex problems through…
Zeroth-order optimization (ZO) typically relies on two-point feedback to estimate the unknown gradient of the objective function. Nevertheless, two-point feedback can not be used for online optimization of time-varying objective functions,…
We present a unified treatment of the abstract problem of finding the best approximation between a cone and spheres in the image of affine transformations. Prominent instances of this problem are phase retrieval and source localization. The…
In this paper, a distributed optimization problem with general differentiable convex objective functions is studied for single-integrator and double-integrator multi-agent systems. Two distributed adaptive optimization algorithm is…
We introduce a general framework for large-scale model-based derivative-free optimization based on iterative minimization within random subspaces. We present a probabilistic worst-case complexity analysis for our method, where in particular…
In this paper we present a new fast and accurate method for Radial Basis Function (RBF) approximation, including interpolation as a special case, which enables us to effectively find the optimal value of the RBF shape parameter. In…