Solving mixed-integer nonlinear optimization problems (MINLPs) to global optimality is extremely challenging. An important step for enabling their solution consists in the design of convex relaxations of the feasible set. Known solution approaches based on spatial branch-and-bound become more...

The computation of lower bounds via the solution of convex lower bounding problems depicts current state-of-the-art in deterministic global optimization. Typically, the nonlinear convex relaxations are further underestimated through linearizations of the convex underestimators at one or several...

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This paper presents a novel partially distributed outer approximation algorithm, named PaDOA, for solving a class of structured mixed integer convex programming problems to global optimality. The proposed scheme uses an iterative outer approximation method for coupled mixed integer optimization...

Lipschitz continuity of the gradient mapping of a continuously differentiable function plays a crucial role in designing various optimization algorithms. However, many functions arising in practical applications such as low rank matrix factorization or deep neural network problems do not have a...

This article is dedicated to the weight set decomposition of a multiobjective (mixed-)integer linear problem with three objectives. We propose an algorithm that returns a decomposition of the parameter set of the weighted sum scalarization by solving biobjective subproblems via Dichotomic Search...

This paper presents a new two-phase method for solving convex mixed-integer nonlinear programming (MINLP) problems, called Decomposition-based Outer Approximation Algorithm (DECOA). In the first phase, a sequence of linear integer relaxed sub-problems (LP phase) is solved in order to rapidly...

The problem of minimizing the difference of two convex functions is called polyhedral d.c. optimization problem if at least one of the two component functions is polyhedral. We characterize the existence of global optimal solutions of polyhedral d.c. optimization problems. This result is used to...

We consider the problem of verifying linear properties of neural networks. Despite their success in many classification and prediction tasks, neural networks may return unexpected results for certain inputs. This is highly problematic with respect to the application of neural networks for...