Nonlinear Model Predictive Control with an Infinite Horizon Approximation

Categories Chemical Engineering, Control Applications, Nonlinear Optimization Tags , , , ,

Current nonlinear model predictive control (NMPC) strategies are formulated as finite predictive horizon nonlinear programs (NLPs), which maintain NMPC stability and recursive feasibility through the construction of terminal cost functions and/or terminal constraints. However, computing these terminal properties may pose formidable challenges with a fixed horizon, particularly in the context of nonlinear dynamic processes. Motivated … Read more

Active-Set Identification in Noisy and Stochastic Optimization

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

Identifying active constraints from a point near a local minimizer is important both theoretically and practically in constrained continuous optimization as it can help identify optimal Lagrange multipliers and essentially reduce an inequality-constrained problem to an equality-constrained one. Traditional active-set identification guarantees have been proved under various types of constraint qualifications. Importantly, they also assume … Read more

AS-BOX: Additional Sampling Method for Weighted Sum Problems with Box Constraints

Categories Bound-constrained Optimization, Nonlinear Optimization Tags , , , , ,

A class of optimization problems characterized by a weighted finite-sum objective function subject to box constraints is considered. We propose a novel stochastic optimization method, named AS-BOX (Additional Sampling for BOX constraints), that combines projected gradient directions with adaptive variable sample size strategies and nonmonotone line search. The method dynamically adjusts the batch size based … Read more

Asynchronous Adaptive Gradient Tracking Methods for Distributed Stochastic Optimization Problems with Decision-dependent Distributions

Categories Stochastic Programming Tags , , ,

This paper proposes a distributed asynchronous adaptive gradient tracking method, DASYAGT, to solve the distributed stochastic optimization problems with decision-dependent distributions over directed graphs. DASYAGT employs the local adaptive gradient to estimate the gradient of the objective function and introduces the auxiliary running-sum variable to handle asynchrony. We show that the iterates generated by DASYAGT … Read more

Gradient Tracking Methods for Distributed Stochastic Optimization Problems with Decision-dependent Distributions

Categories Stochastic Programming Tags , , , ,

This paper aims to seek the performative stable solution and the stationary point of the distributed stochastic optimization problem with decision-dependent distributions, which is a finite-sum stochastic optimization problem over a network and the distribution depends on the decision variables. For the performative stable solution, we propose a distributed algorithm, DSGTD-GD, which combines the distributed … Read more

Greedy Algorithms with Imprecise Oracles for Submodular Knapsack Problems

Categories Approximation Algorithms, Combinatorial Optimization Tags , , ,

We consider the problem of maximizing a monotone increasing, normalized, and submodular function defined on a set of weighted items under a knapsack constraint. A well-known greedy algorithm, analyzed by Wolsey (1982), achieves an approximation factor of \(0.357\) for this problem. This greedy algorithm starts with an empty solution set and iteratively generates a feasible … Read more

Active-set Newton-MR methods for nonconvex optimization problems with bound constraints

Categories Bound-constrained Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

This paper presents active-set methods for minimizing nonconvex twice-continuously differentiable functions subject to bound constraints. Within the faces of the feasible set, we employ descent methods with Armijo line search, utilizing approximated Newton directions obtained through the Minimum Residual (MINRES) method. To escape the faces, we investigate the use of the Spectral Projected Gradient (SPG) … Read more

Assessing Green Hydrogen Production via Offshore Wind in the Dutch North Sea: Complementing Techno-Economic Simulation With Machine Learning and Optimization

Categories Applications - OR and Management Sciences, Energy, Optimization of Simulated Systems Tags , , ,

As countries seek to decarbonize their energy systems, green hydrogen has emerged as a promising energy carrier. This paper studies the production of green hydrogen from offshore wind in the Dutch North Sea, with particular emphasis on understanding how system design decisions and uncertain parameters affect key performance indicators. The analysis builds on a detailed … Read more

On Subproblem Tradeoffs in Decomposition and Coordination of Multiobjective Optimization Problems

Categories Multi-Criteria Optimization

We propose a two-stage methodology to support decision-making for large/complex multiobjective optimization problems (MOPs) with a decomposable structure, regardless of whether the MOP, due to its size, is solvable in its entirety. During the first stage, the MOP is decomposed into a collection of multiobjective subproblems each of which have fewer objectives than the original … Read more

Integrated Bus Fleet Electrification Planning Through Accelerated Logic-Based Benders Decomposition and Restriction Heuristics

Categories (Mixed) Integer Linear Programming, Facility Planning and Design, Transportation Tags , ,

To meet sustainability goals and regulatory requirements, transit agencies worldwide are planning partial and complete transitions to electric bus fleets. This paper presents the first comprehensive and computationally efficient multi-period optimization framework integrating the key planning decisions necessary to support such electrification initiatives. Our model, formulated as a two-stage integer program with integer subproblems, jointly … Read more