# A review of recent advances in global optimization

@article{Floudas2009ARO, title={A review of recent advances in global optimization}, author={Christodoulos A. Floudas and Chrysanthos E. Gounaris}, journal={Journal of Global Optimization}, year={2009}, volume={45}, pages={3-38} }

This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998–2008). It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization with grey box/nonfactorable models, and bilevel nonlinear optimization.

## 441 Citations

### A Review of Deterministic Optimization Methods in Engineering and Management

- Computer Science, Business
- 2012

Recent advances in deterministic methods for solving signomial programming problems and mixed-integer nonlinear programming problems are introduced and important applications of these methods are reviewed to reveal the usefulness of the optimization methods.

### The Robust Constant and Its Applications in Global Optimization

- Computer Science
- 2015

This paper introduced a new concept, robust constant, to quantitatively characterize robustness of measurable sets and measurable functions, and showed that robust constant had significant value in the analysis of some random search algorithms for solving global optimization problem.

### Continuous Global Optimization in R

- Mathematics
- 2014

A new R package globalOptTests is presented that provides a set of standard test problems for continuous global optimization based on C functions by Ali, Khompatraporn, and Zabinsky (2005).

### Review of Mixed‐Integer Nonlinear and Generalized Disjunctive Programming Methods

- Computer Science, Mathematics
- 2014

An overview for deriving MINLP formulations through generalized disjunctive programming (GDP), which is an alternative higher-level representation of MINLP problems, is presented and a review of solution methods for GDP problems is provided.

### Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

- Computer ScienceEur. J. Oper. Res.
- 2016

### Global Optimization of Mixed-Integer ODE Constrained Network Problems Using the Example of Stationary Gas Transport

- MathematicsSIAM J. Optim.
- 2019

A new approach for finding global solutions for a class of mixed-integer nonlinear optimization problems with ordinary differential equation (ODE) constraints on networks is proposed.

### A Review of Particle Swarm Optimization

- Computer Science
- 2018

An overview of the research progress in Particle Swarm Optimization during 1995-2017 is presented, which includes improvements, modifications and applications of this technique.

### Univariate geometric Lipschitz global optimization algorithms

- Mathematics
- 2012

In this survey, univariate global optimization problems are
considered where the objective function or its first derivative
can be multiextremal black-box costly functions satisfying the
Lipschitz…

### The robust constant and its applications in random global search for unconstrained global optimization

- Computer ScienceJ. Glob. Optim.
- 2016

This paper shows that, from the respects of convergence theory and numerical computational cost, robust constant is valuable significantly for analyzing random global search methods for unconstrained global optimization.

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