A collection of test problems for constrained global optimization algorithms
A collection of test problems for constrained global optimization algorithms
Homotopy-continuation algorithm for global optimization
Recent advances in global optimization
Primal-relaxed dual global optimization approach
Journal of Optimization Theory and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
Conditions for Global Optimality 2
Journal of Global Optimization
A review of recent advances in global optimization
Journal of Global Optimization
Using bifurcation branches in complex domain to get multiple solutions
CA '07 Proceedings of the Ninth IASTED International Conference on Control and Applications
Using bifurcation branches in complex domain to get multiple solutions
MNT '07 The IASTED International Conference on Modern Nonlinear Theory: Bifurcation and Chaos
Primal-dual interior-point method for thermodynamic gas-particle partitioning
Computational Optimization and Applications
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This paper addresses the problem of finding the number, K,of phases present at equilibrium and their composition, in a chemicalmixture of n_s substances. This corresponds to the globalminimum of the Gibbs free energy of the system, subject to constraintsrepresenting m_b independent conserved quantities, wherem_b=n_s when no reaction is possible and m_b ≤n_e+1 when reaction is possible and n_e is the number ofelements present. After surveying previous work in the field and pointingout the main issues, we extend the necessary and sufficient condition forglobal optimality based on the ’’reaction tangent-plane criterion‘‘, to thecase involving different thermodynamical models (multiple phase classes). Wethen present an algorithmic approach that reduces this global optimizationproblem (involving a search space of m_b(n_s-1) dimensions) toa finite sequence of local optimization steps inK(n_s-1)-space, K ≤ m_b, and globaloptimization steps in (n_s-1)-space. The global step uses thetangent-plane criterion to determine whether the current solution isoptimal, and, if it is not, it finds an improved feasible solution eitherwith the same number of phases or with one added phase. The global step alsodetermines what class of phase (e.g. liquid or vapour) is to be added, ifany phase is to be added. Given a local minimization procedure returning aKuhn–Tucker point and a global optimization procedure (for alower-dimensional search space) returning a global minimum, the algorithm isproved to converge to a global minimum in a finite number of the above localand global steps. The theory is supported by encouraging computationalresults.