We obtain necessary and sufficient conditions for local Lipschitz-like property and sufficient conditions for local metric regularity in Robinson’s sense of Karush–Kuhn–Tucker point set maps of trust-region subproblems in trust-region methods. The main tools being used in our investigation...

We propose two restricted memory level bundle-like algorithms for minimizing a convex function over a convex set. If the memory is restricted to one linearization of the objective function, then both algorithms are variations of the projected subgradient method. The first algorithm, proposed in...

We provide a first-order necessary and sufficient condition for optimality of lower semicontinuous functions on Banach spaces using the concept of subdifferential. From the sufficient condition we derive that any subdifferential operator is monotone absorbing, hence maximal monotone when the...

This paper is devoted to the study of the first-order behavior of the value function of a parametric discrete optimal control problem with nonconvex cost functions and control constraints. By establishing an abstract result on the Mordukhovich subdifferential of the value function of a...

In branch and bound algorithms in constrained global optimization, a sharp upper bound on the global optimum is important for the overall efficiency of the branch and bound process. Software to find local optimizers, using floating point arithmetic, often computes an approximately feasible point...

In this paper, we investigate the use of DC (Difference of Convex functions) models and algorithms in the application of trust-region methods to the solution of a class of nonlinear optimization problems where the constrained set is closed and convex (and, from a practical point of view, where...

We consider a production planning problem where the production process creates a mixture of desirable products and undesirable byproducts. In this production process, at any point in time the fraction of the mixture that is an undesirable byproduct increases monotonically as a function of the...

We address nonconvex mixed-integer bilinear problems where the main challenge is the computation of a tight upper bound for the objective function to be maximized. This can be obtained by using the recently developed concept of multiparametric disaggregation following the solution of a...

In this paper, we consider a particular class of variational relation problem namely linear variational relation problem wherein the sets are defined by linear inequalities. The purpose is to study the existence of the solution set and its nature for this class of problem. Using these results,...

In this paper, we present a novel algorithm for the solution of multiparametric mixed integer linear programming (mp-MILP) problems that exhibit uncertain objective function coefficients and uncertain entries in the right-hand side constraint vector. The algorithmic procedure employs a branch...