On the Uses of Linear-Quadratic Methods in Solving Nonlinear Dynamic Optimization Problems With Direct Transcription

2021 ◽  
Author(s):  
Daniel Herber ◽  
Athul Sundarrajan
Keyword(s):  
Dynamic Optimization ◽  
Nonlinear Dynamic ◽  
Optimization Problems ◽  
Dynamic Optimization Problems ◽  
Linear Quadratic ◽  
Direct Transcription

On the Uses of Linear-Quadratic Methods in Solving Nonlinear Dynamic Optimization Problems With Direct Transcription

2020 ◽  
Author(s):  
Daniel R. Herber ◽  
Athul K. Sundarrajan
Keyword(s):  
Dynamic Optimization ◽  
Nonlinear Dynamic ◽  
Optimal Control Problems ◽  
Optimization Problems ◽  
Control Problems ◽  
Linear Quadratic ◽  
Direct Transcription ◽  
Solution Strategies ◽  
Engineered Systems ◽  
Direct Incorporation

Abstract Solving nonlinear dynamic optimization (NLDO) and optimal control problems can be quite challenging, but the need for effective methods is ever increasing as more engineered systems become more dynamic and integrated. In this article, we will explore the various uses of linear-quadratic dynamic optimization (LQDO) in the direct transcription-based solution strategies for NLDO. Three general LQDO-based strategies are discussed, including direct incorporation, two-level optimization, and quasi-linearization. Connections are made between a variety of existing approaches, including sequential quadratic programming. The case studies are solved with the various methods using a publicly available, MATLAB-based tool. Results indicate that the LQDO-based strategies can improve existing solvers and be effective solution strategies. However, there are robustness issues and problem derivative requirements that must be considered.

scholarly journals A class of linear quadratic dynamic optimization problems with state dependent constraints

2019 ◽  
Vol 91 (2) ◽  
pp. 325-355 ◽  
Author(s):  
Rajani Singh ◽  
Agnieszka Wiszniewska-Matyszkiel
Keyword(s):  
Optimal Control ◽  
Dynamic Optimization ◽  
Optimization Problems ◽  
Renewable Resource ◽  
Forest Harvesting ◽  
Theoretical Point ◽  
Dynamic Optimization Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
State Dependent

Abstract In this paper, we analyse a wide class of discrete time one-dimensional dynamic optimization problems—with strictly concave current payoffs and linear state dependent constraints on the control parameter as well as non-negativity constraint on the state variable and control. This model suits well economic problems like extraction of a renewable resource (e.g. a fishery or forest harvesting). The class of sub-problems considered encompasses a linear quadratic optimal control problem as well as models with maximal carrying capacity of the environment (saturation). This problem is also interesting from theoretical point of view—although it seems simple in its linear quadratic form, calculation of the optimal control is nontrivial because of constraints and the solutions has a complicated form. We consider both the infinite time horizon problem and its finite horizon truncations.

An algorithm comparison for dynamic optimization problems

2012 ◽  
Vol 12 (10) ◽  
pp. 3176-3192 ◽  
Author(s):  
Ignacio G. del Amo ◽  
David A. Pelta ◽  
Juan R. González ◽  
Antonio D. Masegosa
Keyword(s):  
Dynamic Optimization ◽  
Optimization Problems ◽  
Dynamic Optimization Problems ◽  
Algorithm Comparison
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