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In this paper, we propose a smoothing method to solve nonlinear complementarity problems involving P 0-functions. We propose a nonparametric algorithm to solve the nonlinear corresponding system of equations and prove some global and local…
This paper focuses on stochastic proximal gradient methods for optimizing a smooth non-convex loss function with a non-smooth non-convex regularizer and convex constraints. To the best of our knowledge we present the first non-asymptotic…
This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider…
In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…
Based on smoothing techniques, we propose two new methods to solve linear complementarity problems (LCP) called TLCP and Soft-Max. The idea of these two new methods takes inspiration from interior-point methods in optimization. The…
This paper presents a geometric approach to the classical isoperimetric problem by analysing the efficiency of regular polygons in enclosing maximum area for a fixed perimeter. Using efficiency metrics, it proves that regular polygons…
As science and engineering have become increasingly data-driven, the role of optimization has expanded to touch almost every stage of the data analysis pipeline, from signal and data acquisition to modeling and prediction. The optimization…
Smoothing methods have become part of the standard tool set for the study and solution of nondifferentiable and constrained optimization problems as well as a range of other variational and equilibrium problems. In this note we synthesize…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…
Trimming is a core technique in geometric modeling. Unfortunately, the resulting objects do not take the requirements of numerical simulations into account and yield various problems. This paper outlines principal issues of trimmed models…
Approximating a function with a finite series, e.g., involving polynomials or trigonometric functions, is a critical tool in computing and data analysis. The construction of such approximations via now-standard approaches like least squares…
In this work, we consider convex optimization problems with smooth objective function and nonsmooth functional constraints. We propose a new stochastic gradient algorithm, called Stochastic Halfspace Approximation Method (SHAM), to solve…
This paper considers non-smooth optimization problems where we seek to minimize the pointwise maximum of a continuously parameterized family of functions. Since the objective function is given as the solution to a maximization problem,…
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…
Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the…
In this article we propose a method for solving unconstrained optimization problems with convex and Lipschitz continuous objective functions. By making use of the Moreau envelopes of the functions occurring in the objective, we smooth the…
This paper is devoted to discuss some of the features of self-similar solutions of the first kind. We consider the cylindrically symmetric solutions with different homotheties. We are interested in evaluating the quantities acceleration,…
This paper develops a smoothing-based postprocessing method for superconvergence in finite element methods. The method applies a few smoothing iterations, such as damped Jacobi, Gauss-Seidel, or conjugate gradient, with initial guess being…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
In this article, we introduce the notion of stochastic symmetry of a differential equation. It consists in a stochastic flow that acts over a solution of a differential equation and produces another solution of the same equation. In the…