The term probabilistic constrained programming means the same as chance constrained programming, i.e., optimization of a function subject to certain conditions where at least one is formulated so that a condition, involving random variables, should hold with a prescribed probability. The probability is usually not prescribed exactly but a lower bound is given instead which is in practice near u...

An algorithm for solving large nonlinear optimization problems with simple bounds is de scribed It is based on the gradient projection method and uses a limited memory BFGS matrix to approximate the Hessian of the objective function It is shown how to take advan tage of the form of the limited memory approximation to implement the algorithm e ciently The results of numerical tests on a set of l...

The optimization of noisy functions is a common problem occurring in various applications. In this paper, a new approach is presented for low-dimensional bound constrained problems, based on the use of quadratic models and a restriction of the evaluation points to successively refined grids. In the noiseless case, global convergence of the algorithm to a stationary point is proved; in the noisy...

Geometric branch-and-bound methods are popular solution algorithms in deterministic global optimization to solve problems in small dimensions. The aim of this paper is to formulate a geometric branch-and-bound method for constrained global optimization problems which allows the use of arbitrary bounding operations. In particular, our main goal is to prove the convergence of the suggested method...

We provide a monotone non increasing sequence of upper bounds f k (k ≥ 1) converging to the global minimum of a polynomial f on simple sets like the unit hypercube. The novelty with respect to the converging sequence of upper bounds in [J.B. Lasserre, A new look at nonnegativity on closed sets and polynomial optimization, SIAM J. Optim. 21, pp. 864–885, 2010] is that only elementary computation...

We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound constraints where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective function can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems arises frequ...

In this paper we propose a filter-trust-region algorithm for solving nonlinear optimization problems with simple bounds. It extends the technique of Gould, Sainvitu and Toint [15] designed for unconstrained optimization. The two main ingredients of the method are a filter-trust-region algorithm and the use of a gradient-projection method. The algorithm is shown to be globally convergent to at l...

1. Abstract Practical optimization problems often involve nonsmooth functions of hundreds or thousands of variables. As a rule, the variables in such large problems are restricted to certain meaningful intervals. In the report [Haarala, Mäkelä, 2006] we have described an efficient adaptive limited memory bundle method for large-scale nonsmooth, possibly nonconvex, bound constrained optimization...

Termination criteria for the iterative solution of bound-constrained optimization problems are examined in the light of backward error analysis. It is shown that the problem of determining a suitable perturbation on the problem’s data corresponding to the definition of the backward error is analytically solvable under mild assumptions. Moreover, a link between existing termination criteria and ...

We consider the solution of bound constrained optimization problems, where we assume that the evaluation of the objective function is costly, its derivatives are unavailable and the use of exact derivativefree algorithms may imply a too large computational burden. There is plenty of real applications, e.g. several design optimization problems [1,2], belonging to the latter class, where the obje...