Recall we were considering the problem minz∈Rn p(z) where p(z) is a degree 2m polynomial such that p(z) = ∑ |α|≤2m pαz , where α = (α1, . . . , αn) is a vector of exponents, using the notation that z = z1 1 . . . z αn n . One equivalent way of expressing this problem is to notice this is the same as minimizing ∫ p(z)μ(dz) over the set of all probability distributions μ and note that it’s equiva...

In this paper we consider a global optimization approach for solving fuzzy fractional posynomial geometric programming problems. The problem of concern involves positive trapezoidal fuzzy numbers in the objective function. For obtaining an optimal solution, Dinkelbach’s algorithm which achieves the optimal solution of the optimization problem by means of solving a sequence of subproblems ...

In this paper‎, ‎two extended three-term conjugate gradient methods based on the Liu-Storey ({tt LS})‎ ‎conjugate gradient method are presented to solve unconstrained optimization problems‎. ‎A remarkable property of the proposed methods is that the search direction always satisfies‎ ‎the sufficient descent condition independent of line search method‎, ‎based on eigenvalue analysis‎. ‎The globa...

In this paper a hybrid algorithm based on exploration power of the Genetic algorithms and exploitation capability of Nelder Mead simplex is presented for global optimization of multi-variable functions. Some modifications are imposed on genetic algorithm to improve its capability and efficiency while being hybridized with Simplex method. Benchmark test examples of structural optimization with a...

12 Our view is that no general purpose algorithm should be expected to eeciently nd global mini-mizers of nonconvex continuous optimization problems. We submit that eecient global optimization is generally impossible|see, for example, Stephens and Baritompa (1998) and Anonymous (1972). But this does not mean that one should not endeavor to devise algorithms for speciic global optimization probl...

My thesis focuses on global optimization of nonconvex integral objective functions subject to parameter dependent ordinary differential equations. In particular, efficient, deterministic algorithms are developed for solving problems with both linear and nonlinear dynamics embedded. The techniques utilized for each problem classification are unified by an underlying composition principle transfe...

A desire with iterative optimization techniques is that the algorithm reaches the global optimum rather than get stranded at a local optimum value. In this paper, we examine the theoretical and numerical global convergence properties of a certain “gradient free” stochastic approximation algorithm called “SPSA,” that has performed well in complex optimization problems. We establish two theorems ...

Accurate modelling of real-world problems often requires nonconvex terms to be introduced in the model, either in the objective function or in the constraints. Nonconvex programming is one of the hardest fields of optimization, presenting many challenges in both practical and theoretical aspects. The presence of multiple local minima calls for the application of global optimization techniques. ...

Recently a general mathematical framework has been developed [3] for studying mathematical programming problems described by means of increasing functions, or more generally, differences of increasing functions. It has been shown in [3] that any mathematical programming problem of this class can be reduced to an equivalent problem of the following form, called canonical monotonic optimization p...

We consider a combination of state space partitioning and random search methods for solving deterministic global optimization problem. We assume that function computations are costly and nding global optimum is diicult. Therefore, we may decide to stop searching long before we found a solution close to the optimum. Final reward of the algorithm is deened as the best found function value minus t...