Author

M. Alamir

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Preprint Sep 2026

A Unified Efficient Gradient-Based Heuristic For Box-Constrained Expectation-Related and Risk-Averse Stochastic Optimization Problems

This paper presents a new algorithm addressing the problem of stochastic optimization where the cost function depends on a vector of uncertain parameters with known statistics. The algorithm is parameterized so as to address various stochastic formulations spanning from Expectation-focused to Value-at-Risk (VaR) as well as Conditional-Value-at-Risk (CVaR)-focused formulations. The algorithm leverages a recently proposed gradient-based Search&Accelerate algorithm which is originally dedicated to deterministic optimization problems. The approach is based on a sequence of warm-started solutions of instances of the problem. These solutions together with a samples of other solutions belonging to the convex hull of the first ones constitute the set of admissible candidates. Among this discrete set of candidates, the optimal solution is selected with regards to a sample-based approximation of the targeted criterion. The relevance of the algorithm and its efficiency are discussed and shown using a tailored illustrative example.

M. Alamir · 0 citations

Preprint Jul 2026

A Nonlinear Model Predictive Control Perspective on Gradient-Based Optimization: A New Efficient, Parameter-Free and Provably Stable Algorithm

This paper discusses some aspects related to gradient-based optimization algorithms with special focus on the requirements associated to their use in the implementation of Nonlinear Model Predictive Control. Based on a dedicated discussion, a new algorithm, termed Search and Accelerate (SaA) is proposed that mixes together a novel line search, a trust region mechanism together with an adaptation of the gradient acceleration scheme. A dedicated benchmark involving a set of 600 instances of box constrained optimization problems is designed and used in order to show the algorithm performances which make it a highly competitive general purpose gradient-based alternative for box-constrained optimization problems. An appealing feature of the algorithm is its robustness to the choice of the few parameters involved in its definition making the default values a valid option for any problem without a priori knowledge of the related Lipchitz constant. Moreover, an example of use of the proposed algorithm in NMPC implementation is proposed showing the possibility to reduce the control updating period which might be mandatory in some circumstances.

M. Alamir · 0 citations