On multi-parametric programming and its applications in process systems engineering

R Oberdieck, NA Diangelakis, I Nascu… - … research and design, 2016 - Elsevier
In multi-parametric programming, an optimization problem is solved for a range and as a
function of multiple parameters. In this review, we discuss the main developments of multi …

Multiparametric programming in process systems engineering: Recent developments and path forward

I Pappas, D Kenefake, B Burnak… - Frontiers in Chemical …, 2021 - frontiersin.org
The inevitable presence of uncertain parameters in critical applications of process
optimization can lead to undesirable or infeasible solutions. For this reason, optimization …

Bilevel optimization: theory, algorithms, applications and a bibliography

S Dempe - Bilevel optimization: advances and next challenges, 2020 - Springer
Bilevel optimization problems are hierarchical optimization problems where the feasible
region of the so-called upper level problem is restricted by the graph of the solution set …

Pop–parametric optimization toolbox

R Oberdieck, NA Diangelakis… - Industrial & …, 2016 - ACS Publications
In this paper, we describe POP, a MATLAB toolbox for parametric optimization. It features (a)
efficient implementations of multiparametric programming problem solvers for …

On unbounded and binary parameters in multi-parametric programming: applications to mixed-integer bilevel optimization and duality theory

R Oberdieck, NA Diangelakis, S Avraamidou… - Journal of Global …, 2017 - Springer
In multi-parametric programming an optimization problem is solved as a function of certain
parameters, where the parameters are commonly considered to be bounded and …

Explicit machine learning-based model predictive control of nonlinear processes via multi-parametric programming

W Wang, Y Wang, Y Tian, Z Wu - Computers & Chemical Engineering, 2024 - Elsevier
Abstract Machine learning-based model predictive control (ML-MPC) has been developed to
control nonlinear processes with unknown first-principles models. While ML models can …

Deterministic solution approach for some classes of nonlinear multilevel programs with multiple followers

AM Kassa, SM Kassa - Journal of Global Optimization, 2017 - Springer
In this paper we investigate multilevel programming problems with multiple followers in each
hierarchical decision level. It is known that such type of problems are highly non-convex and …

Three-level global resource allocation model for HIV control: a hierarchical decision system approach

SM Kassa - Mathematical Biosciences & Engineering, 2018 - aimsciences.org
Funds from various global organizations, such as, The Global Fund, The World Bank, etc.
are not directly distributed to the targeted risk groups. Especially in the so-called third-world …

[图书][B] Multi-level Mixed-Integer Optimization: Parametric Programming Approach

S Avraamidou, E Pistikopoulos - 2022 - books.google.com
This book provides the fundamental underlying mathematical theory, numerical algorithms
and effi cient computational tools for the solution of multi-level mixedinteger optimization …

A relaxation solving approach for the linear trilevel programming problem

Y Lv, J Jiang - Computational and Applied Mathematics, 2021 - Springer
In this paper, the global and local optimal solutions of the linear trilevel programming
problem are concerned. First, we replace the lower level problem with its optimality …