Modified projected Newton scheme for non-convex function with simple constraints

Optimizing Costly Functions with Simple Constraints: A Limited-Memory Projected Quasi-Newton Algorithm

An optimization algorithm for minimizing a smooth function over a convex set is described. Each iteration of the method computes a descent direction by minimizing, over the original constraints, a diagonal plus lowrank quadratic approximation to the function. The quadratic approximation is constructed using a limited-memory quasi-Newton update. The method is suitable for large-scale problems wh...

A Modified Relaxation Scheme for Mathematical Programs with Complementarity Constraints

Regularization With Non-convex Separable Constraints

We consider regularization of nonlinear ill-posed problems with constraints which are non-convex. As a special case we consider separable constraints, i.e. the regularization takes place in a sequence space and the constraint acts on each sequence element with a possibly non-convex function. We derive conditions under which such a constraint provides a regularization. Moreover, we derive estima...

Convex drawings of graphs with non-convex boundary constraints

In this paper, we study a new problem of convex drawing of planar graphs with non-convex boundary constraints. It is proved that every triconnected plane graph whose boundary is fixed with a star-shaped polygon admits a drawing in which every inner facial cycle is drawn as a convex polygon. We also prove that every four-connected plane graph whose boundary is fixed with a crown-shaped polygon a...

Nonparametric instrumental regression with non-convex constraints

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variab...