Different strategies for defining the relationship between feasible and infeasible individuals in evolutionary algorithms can provide with very different results when solving numerical constrained optimization problems. This paper proposes a novel EA to balance the relationship between feasible and infeasible individuals to solve numerical constrained optimization problems. According to the fea...

In the paper a primal-infeasible interior point algorithm is proposed for linearly constrained convex programming. The starting point is any positive primal-infeasible dual-feasible point in a large region. The method maintains positivity of the iterates which point satisfies primalinfeasible dual-feasible point. At each iterates it requires to solve approximately a nonlinear system. It is show...

The Noodle method allows a fast and efficient sampling of the region of integration during Monte Carlo calculations. The method works by automatically optimizing the weight distribution and by replacing analytic results by exact numerical calculations. The method allows integrations of certain functions that have been heretofore considered infeasible.

A wide variety of analysis and design problems arising in control, communication and information theory, statistics, computational geometry and many other elds can be expressed as semide nite programming problems (SDPs) or determinant maximization problems (maxdet-problems). In engineering applications these problems usually have matrix structure, i.e., the optimization variables are matrices. ...

Beside the curse of dimensionality and imbalanced classes, unfavorable data distributions can hamper classification accuracy. This is particularly problematic with increasing dimensionality of the classification task. A classifier that can handle high-dimensional and imbalanced data sets is the cascade classification method for time series. The cascade classifier can compound unfavorable data d...

We propose pivot methods that solve linear programs by trying to close the duality gap from both ends. The first method maintains a set B of at most three bases, each of a different type, in each iteration: a primal feasible basis Bp, a dual feasible basis Bd and a primal-and-dual infeasible basis Bi. From each B ∈ B, it evaluates the primal and dual feasibility of all primal and dual pivots to...

In this paper, we propose a Mizuno-Todd-Ye predictor-corrector infeasible-interior-point method for symmetric optimization using the arc-search strategy. The proposed algorithm searches for optimizers along the ellipses that approximate the central path and ensures that the duality gap and the infeasibility have the same rate of decline. By analyzing, we obtain the iteration complexity [Formula...

The search directions in an interior-point method for large scale semidefinite programming (SDP) can be computed by applying a Krylov iterative method to either the Schur complement equation (SCE) or the augmented equation. Both methods suffer from slow convergence as interior-point iterates approach optimality. Numerical experiments have shown that diagonally preconditioned conjugate residual ...

In this paper, we outline a bilevel approach for solving mixed integer nonlinear programming problems. The approach combines a branch-and-bound algorithm in the outer iterations and an infeasible interior-point method in the inner iterations. We report on the details of the implementation, including the efficient pruning of the branch-and-bound tree via equilibrium constraints, warmstart strate...