Constrained Nonlinear Optimization

Stochastic Augmented Lagrangian Framework with Second-Order Convergence Guarantees for Nonconvex Expectation-Constrained Optimization

Published: 2026/09/23

In this paper, we propose and analyze an augmented Lagrangian framework for solving stochastic nonconvex optimization problems with expectation-based equality constraints over a closed and convex constraint set. The framework generates a sequence of nonconvex primal subproblems, which are solved inexactly using stochastic second-order methods. We establish iteration complexity results for obtaining approximate second-order stationary … Read more

A branch-and-bound algorithm for the computation of optimal point mappings of parametric optimization problems

Published: 2026/09/22

Constrained Nonlinear Optimization, Global Optimization Branch-and-Bound, global optimization, minimal point mapping, non-convex optimization, parametric optimization

We propose a novel branch‑and‑bound algorithm that constructs rigorous outer approximations of the optimal point mapping for parametric optimization problems with guaranteed feasibility and optimality tolerances. The method uses the improvement‑function reformulation to define discarding and inclusion tests on sub-boxes, constructing a rigorous outer approximation. Under the same regularity conditions that ensure exactness of this … Read more

A Computational Toolbox for Linear Optimization with Joint Affine Chance Constraints

Published: 2026/09/21

Constrained Nonlinear Optimization, Linear Programming, Optimization Software Benchmark computational toolbox, joint chance constraints, linear programming, proximal methods, spherical--radial decomposition

We present a Julia computational toolbox for linear optimization problems with joint affine chance constraints under elliptically symmetric uncertainty. The toolbox combines a spherical–radial oracle for estimating the joint probability and its gradient with three structured optimization methods: Proximal, Feasible, and Penalty. The oracle supports several elliptically symmetric distributions and is integrated with these methods … Read more

A Proximal Approach for Nonsmooth Composite-Constrained Optimization

Published: 2026/09/11

Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming composite optimization, improvement function, nonsmooth nonconvex optimization, proximal method

We propose a proximal-type algorithm for nonsmooth and nonconvex optimization problems with composite constraints. The constraint is defined by the composition of a locally upper-\(C^2\) outer function with a locally Lipschitz continuous inner mapping. The method is based on an improvement function that balances objective decrease and constraint satisfaction, and on a surrogate model obtained … Read more

An optimal orbit design for LISA

Published: 2026/09/03

Yaguang Yang

Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs constrained nonlinear optimization, formation fly, optimal orbit design

The ESA/NASA joint LISA (laser interferometer space antenna) mission is designed to detect gravitational waves to perform gravitational astronomy. A key mission requirement is the maintenance of a three-spacecraft constellation in a near-equilateral triangular configuration with a prescribed inter-spacecraft separation. Existing approaches have addressed this problem using simplified dynamical models to enhance tractability; however, the … Read more

New inexact adaptive proximal gradient algorithms for nonconvex composite optimization problems

Published: 2026/08/31

Pham Thi Hoai

Constrained Nonlinear Optimization, Nonlinear Optimization adaptive proximal gradient, composite optimization problems, inexact proximal gradient algorithms, nonconvex optimization, nonlinear programming

In this paper, we propose new inexact adaptive proximal gradient algorithms for solving nonconvex composite optimization problems, where the objective is the sum of a differentiable nonconvex function and a convex non-differentiable function. A new relative error criterion to compute the proximal operator inexactly has been proposed together with new adaptive strate- gies for selecting … Read more

An Adaptive Augmented Lagrangian Method for Deterministic and Stochastic Nonconvex Optimization

Published: 2026/08/27

Constrained Nonlinear Optimization, Stochastic Programming augmented Lagrangian, nonlinear optimization, stochastic optimization, worst-case complexity

We present an inexact Augmented Lagrangian algorithm for solving nonlinear, non-convex optimization problems. Unlike most recently proposed Augmented Lagrangian methods with worst-case complexity guarantees, we utilize adaptive penalty parameter updates and full dual stepsizes. We show that the method matches the best known worst-case complexity results for Augmented Lagrangian methods (up to logarithmic factors) when … Read more

Combining Reinforcement Learning with Arc-search Interior-Point Method for Path Planning

Published: 2026/08/21

Yaguang Yang

Constrained Nonlinear Optimization, Control Applications, Nonlinear Optimization arc-search, nonlinear optimization, obstacle avoidance, Path planning

Path planning in environments containing obstacles has numerous practical applications. The problem is challenging because it is inherently nonlinear and nonconvex. Consequently, a variety of techniques have been developed to address this problem, among which machine learning and optimal control (or optimization) have emerged as two prominent approaches. In general, machine learning methods do not … Read more

An arc-search interior-point algorithm for nonlinear constrained optimization

Published: 2026/08/20

Yaguang Yang

Constrained Nonlinear Optimization, Nonlinear Optimization arc-search, Interior-point algorithm, nonlinear optimization

This paper proposes a new arc-search interior-point algorithm for the nonlinear constrained optimization problem. The proposed algorithm uses the second-order derivatives to construct a search arc that approaches the optimizer. Because the arc stays in the interior set longer than any straight line, it is expected that the scheme will generate a better new iterate … Read more

A Local-Linearly Convergent Algorithm for Nonconvex Equality-Constrained Optimization

Published: 2026/08/12

Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science

For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.~is an iteration-efficient approach, based on minimizing Fletcher’s augmented Lagrangian function, for finding an approximate second-order stationary point from an arbitrary starting point. In this paper, the analysis of this algorithm is extended, offering a two-fold contribution. First, it is shown that … Read more