Interval partitioning methods for mixed integer nonlinear problems

2014 ◽  
pp. 63-67
Author(s):  
B Ergüneş ◽  
L Özdamar ◽  
N Gülcan ◽  
O Demir
Keyword(s):  
Nonlinear Problems ◽  
Mixed Integer ◽  
Partitioning Methods ◽  
Mixed Integer Nonlinear Problems

Global optimization of mixed-integer nonlinear problems

AIChE Journal ◽  
2000 ◽  
Vol 46 (9) ◽  
pp. 1769-1797 ◽  
Author(s):  
C. S. Adjiman ◽  
I. P. Androulakis ◽  
C. A. Floudas
Keyword(s):  
Global Optimization ◽  
Nonlinear Problems ◽  
Mixed Integer ◽  
Mixed Integer Nonlinear Problems

scholarly journals DOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems

2020 ◽  
Vol 78 (1) ◽  
pp. 1-36 ◽  
Author(s):  
Burcu Beykal ◽  
Styliani Avraamidou ◽  
Ioannis P. E. Pistikopoulos ◽  
Melis Onel ◽  
Efstratios N. Pistikopoulos
Keyword(s):  
Nonlinear Problems ◽  
Data Driven ◽  
Mixed Integer ◽  
Mixed Integer Nonlinear Problems

scholarly journals New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 198
Author(s):  
Loay Alkhalifa ◽  
Hans Mittelmann
Keyword(s):  
Quadratic Programming ◽  
Linear Approximation ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Nonlinear Problems ◽  
Computational Experiments ◽  
Mixed Integer ◽  
Piecewise Linear Approximation ◽  
Quadratically Constrained Quadratic Programming ◽  
Quadratically Constrained

Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform nonlinear problems into linear ones. This paper will introduce PLA with brief a background and literature review, followed by describing our contribution before presenting the results of computational experiments and our findings. The goals of this paper are (a) improving PLA models by using nonuniform domain partitioning, and (b) proposing an idea of applying PLA partially on MINLP problems, making them easier to handle. The computational experiments were done using quadratically constrained quadratic programming (QCQP) and MIQCQP and they showed that problems under PLA with nonuniform partition resulted in more accurate solutions and required less time compared to PLA with uniform partition.

Optimal Test Assembly in Practice

2013 ◽  
Vol 221 (3) ◽  
pp. 190-200 ◽  
Author(s):  
Jörg-Tobias Kuhn ◽  
Thomas Kiefer
Keyword(s):  
Particle Physics ◽  
Large Scale ◽  
Block Design ◽  
Linear Optimization ◽  
Mixed Integer ◽  
Optimal Test ◽  
Automated Test Assembly ◽  
Test Assembly ◽  
Block Level ◽  
Mixed Integer Linear Optimization

Several techniques have been developed in recent years to generate optimal large-scale assessments (LSAs) of student achievement. These techniques often represent a blend of procedures from such diverse fields as experimental design, combinatorial optimization, particle physics, or neural networks. However, despite the theoretical advances in the field, there still exists a surprising scarcity of well-documented test designs in which all factors that have guided design decisions are explicitly and clearly communicated. This paper therefore has two goals. First, a brief summary of relevant key terms, as well as experimental designs and automated test assembly routines in LSA, is given. Second, conceptual and methodological steps in designing the assessment of the Austrian educational standards in mathematics are described in detail. The test design was generated using a two-step procedure, starting at the item block level and continuing at the item level. Initially, a partially balanced incomplete item block design was generated using simulated annealing, whereas in a second step, items were assigned to the item blocks using mixed-integer linear optimization in combination with a shadow-test approach.

Sign in / Sign up

Export Citation Format

Share Document