A review of recent advances in global optimization

  title={A review of recent advances in global optimization},
  author={Christodoulos A. Floudas and Chrysanthos E. Gounaris},
  journal={Journal of Global Optimization},
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. 

A Review of Deterministic Optimization Methods in Engineering and Management

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

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

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

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.

Overview of Optimization

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

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

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

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

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.



Recent developments and trends in global optimization

Global Optimization of Bilevel Programming Problems via Parametric Programming

This paper presents a global optimization approach to a bilevel programming problem which refers to an optimization problem that is constrained by another problem, which can be solved to global optimality for linear- linear, linear-quadratic, quadratic-linear, and quadRatic-quadraatic bileVEL models.

Global Optimization of Nonlinear Bilevel Programming Problems

A novel technique that addresses the solution of the general nonlinear bilevel programming problem to global optimality based on the relaxation of the feasible region by convex underestimation utilizing the basic principles of the deterministic global optimization algorithm, αBB.

Global Optimization: Deterministic Approaches

This study develops a unifying approach to constrained global optimization. It provides insight into the underlying concepts and properties of diverse techniques recently proposed to solve a wide

Introduction to Global Optimization (Nonconvex Optimization and Its Applications)

Global optimization the first textbook on methods computation and lipshitz problems decomposition and the first comprehensive textbook on optimization focus on.

A hybrid global optimization approach for solvent design

Logic-Based Modeling and Solution of Nonlinear Discrete/Continuous Optimization Problems

This paper presents a review of advances in the mathematical programming approach to discrete/continuous optimization problems, particularly Generalized Disjunctive Programming (GDP), which the authors have extensively investigated over the last few years.

On an Efficient Use of Gradient Information for Accelerating Interval Global Optimization Algorithms

Numerical comparison made on a wide set of multiextremal test functions has shown that on average the new algorithm works faster than a traditional interval analysis global optimization method.

Global Solution of Optimization Problems with Dynamic Systems Embedded

Combining the composition technique attributed to McCormick, differential inequalities, and a novel outer approximation technique, convex Relaxations for the integrand are derived and it is shown that convex relaxations for an integrand pointwise in time imply convex relaxedations for a integral.