An implicit function formulation for optimization of discretized index-1 differential algebraic systems

A formulation for the optimization of index-1 differential algebraic equation systems (DAEs) that uses implicit functions to remove algebraic variables and equations from the optimization problem is described. The formulation uses the implicit function theorem to calculate derivatives of functions that remain in the optimization problem in terms of a reduced space of variables, allowing … Read more

MPCC Strategies for Nonsmooth NLPs

This paper develops solution strategies for large-scale nonsmooth optimization problems. We transform nonsmooth programs into equivalent mathematical programs with complementarity constraints (MPCCs), and then employ NLP-based strategies for their so- lution. For this purpose, two NLP formulations based on complementarity relaxations are put forward, one of which applies a parameterized formulation and operates with a … Read more

Dynamic Optimization with Complementarity Constraints: Smoothing for Direct Shooting

We consider optimization of differential-algebraic equations (DAEs) with complementarity constraints (CCs) of algebraic state pairs. Formulating the CCs as smoothed nonlinear complementarity problem (NCP) functions leads to a smooth DAE, allowing for the solution in direct shooting. We provide sufficient conditions for well-posedness. Thus, we can prove that with the smoothing parameter going to zero, … Read more

pyomo.dae: A Modeling and Automatic Discretization Framework for Optimization with Differential and Algebraic Equations

We describe pyomo.dae, an open source Python-based modeling framework that enables high-level abstract specification of optimization problems with differential and algebraic equations. The pyomo.dae framework is integrated with the Pyomo open source algebraic modeling language, and is available at http: //www.pyomo.org. One key feature of pyomo.dae is that it does not restrict users to standard, … Read more

On an inexact trust-region SQP-filter method for constrained nonlinear optimization

A class of trust-region algorithms is developed and analyzed for the solution of optimization problems with nonlinear equality and inequality constraints. Based on composite-step trust region methods and a filter approach, the resulting algorithm also does not require the computation of exact Jacobians; only Jacobian vector products are used along with approximate Jacobian matrices. As … Read more

Optimal Sensitivity Based on IPOPT

We introduce a flexible, open source implementation that provides the optimal sensitivity of solutions of nonlinear programming (NLP) problems, and is adapted to a fast solver based on a barrier NLP method. The program, called sIPOPT evaluates the sensitivity of the KKT system with respect to model parameters. It is paired with the open-source IPOPT … Read more

The Advanced Step NMPC Controller: Optimality, Stability and Robustness

Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for nonlinear model predictive control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on nonlinear … Read more

A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity

Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this … Read more

Modeling and Simulation of Metabolic Networks for Estimation of Biomass Accumulation Parameters

Metabolic networks are defined as the collection of biochemical reactions within a cell that define the functions of that cell. Due to the growing need to understand the functions of biological organisms for industrial and medical purposes, modeling and simulation of metabolic networks has attracted a lot of attention recently. Traditionally, metabolic networks are modeled … Read more

An algorithmic framework for convex mixed integer nonlinear programs

This paper is motivated by the fact that mixed integer nonlinear programming is an important and difficult area for which there is a need for developing new methods and software for solving large-scale problems. Moreover, both fundamental building blocks, namely mixed integer linear programming and nonlinear programming, have seen considerable and steady progress in recent … Read more