Data-Driven Multistage Scheduling Optimization for Refinery Production under Uncertainty: Systematic Framework, Modeling Approach, and Application Analysis

Categories Control Applications, Scheduling, Stochastic Programming Tags , , , , , , ,

The widespread existence of various uncertainties makes the inherently complex refinery production scheduling problem even more challenging. To address this issue, this paper proposes a viable systematic data-driven multistage scheduling optimization framework and develops a corresponding structured modeling methodology. Under this paradigm, unit-level advanced control and plant-level intelligent scheduling are coordinated to jointly deal with … Read more

Gradient Methods with Online Scaling Part I. Theoretical Foundations

Categories Convex Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , ,

This paper establishes the theoretical foundations of the online scaled gradient methods (OSGM), a framework that utilizes online learning to adapt stepsizes and provably accelerate first-order methods. OSGM quantifies the effectiveness of a stepsize by a feedback function motivated from a convergence measure and uses the feedback to adjust the stepsize through an online learning … Read more

A variable dimension sketching strategy for nonlinear least-squares

Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares

We present a stochastic inexact Gauss-Newton method for the solution of nonlinear least-squares. To reduce the computational cost with respect to the classical method, at each iteration the proposed algorithm approximately minimizes the local model on a random subspace. The dimension of the subspace varies along the iterations, and two strategies are considered for its … Read more

A symmetric extrapolated proximal alternating predictor-corrector method for saddle-point problems

Categories Convex Optimization Tags , , , ,

The proximal alternating predictor-corrector (PAPC) method is a widely used first-order algorithm for solving convex-concave saddle-point problems involving both smooth and nonsmooth components. Unlike the primal-dual hybrid gradient (PDHG) method, which incorporates an extrapolation step with parameter $\theta \in (0,1]$ to improve convergence, the existing convergence analysis of PAPC has been limited to the case … Read more

Solving a linear program via a single unconstrained minimization

Categories Linear Programming, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , , ,

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

Retrospective Approximation Sequential Quadratic Programming for Stochastic Optimization with General Deterministic Nonlinear Constraints

Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization in Data Science Tags , , , ,

In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially constructs increasingly accurate approximations of the true problems which are solved to a specified accuracy via a deterministic solver, thereby decoupling the uncertainty from … Read more

A Framework for Explainable Knowledge Generation with Expensive Sample Evaluations

Categories Global Optimization, Multidisciplinary Design Optimization, Optimization of Simulated Systems Tags , , ,

Real world problems often require complex modeling and computation efforts to be effectively addressed. Relying solely on data-driven approaches without integrating physics-based models can result in limited predictive capabilities. Even advanced techniques such as deep learning may be impractical for decision-makers due to the lack of data and challenges in justifying and explaining results. In … Read more

On Multi-Disjunctive Valid Inequalities for Chance-Constrained Stochastic Problems with Finite Support

Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , , , ,

We consider mixed-integer linear chance-constrained problems for which the random vector that parameterizes the feasible region has finite support. Our key objective is to improve branch-and-bound or -cut approaches by introducing new types of valid inequalities that improve the dual bound and, by this, the overall performance of such methods. We introduce so-called multi-disjunctive valid … Read more

Mixed-Feature Logistic Regression Robust to Distribution Shifts

Categories Applications - OR and Management Sciences, Integer Programming, Robust Optimization Tags , , ,

Logistic regression models are widely used in the social and behavioral sciences and in high-stakes domains, due to their simplicity and interpretability properties. At the same time, such domains are permeated by distribution shifts, where the distribution generating the data changes between training and deployment. In this paper, we study a distributionally robust logistic regression … Read more

Stability Regularized Cross-Validation

Categories Data-Mining

We revisit the problem of ensuring strong test-set performance via cross-validation. Motivated by the generalization theory literature, we propose a nested k-fold cross- validation scheme that selects hyperparameters by minimizing a weighted sum of the usual cross-validation metric and an empirical model-stability measure. The weight on the stability term is itself chosen via a nested … Read more