unconstrained minimization – Optimization Online

Rooting Out Self-Intersection: An Algebraic Shape-Optimization Barrier

Published: 2026/09/06

Nima Kakhsaz Malayeri

Applications - Science and Engineering, Multidisciplinary Design Optimization, Nonlinear Optimization barrier penalty function, iterative linear algebra techniques, shape optimization, unconstrained minimization

Self-intersection is a fundamental feasibility constraint in shape optimization: a self-crossing boundary leaves its interior, normal field, and finite-element mesh ill-defined, yet most existing barriers rely on heuristic geometric-proximity measures rather than certifying self-intersection directly. We propose a self-intersection barrier grounded in algebraic detection. We derived two bivariate polynomials from a curve’s Fourier coefficients whose … Read more

Solving a linear program via a single unconstrained minimization

Published: 2025/05/27

Linear Programming, Nonlinear Systems and Least-Squares, Unconstrained Optimization global convergence, linear programming, penalty methods, regularized newton methods, unconstrained minimization, zero residual problem

This paper proposes a novel approach for solving linear programs. We reformulate a primal-dual linear program as an unconstrained minimization of a convex and twice continuously differentiable merit function. When the optimal set of the primal-dual pair is nonempty, its optimal set is equal to the optimal set of the proposed merit function. Minimizing this … Read more