Jan-J. Rückmann

A numerical study of MIDACO on 100 MINLP benchmarks

This article presents a numerical study on MIDACO, a new global optimization software for mixed integer non-linear programming (MINLP) based on ant colony optimization and the oracle penalty method. Extensive and rigorous numerical tests on a set of 100 non-convex MINLP benchmark problems from the open literature are performed. Results obtained by MIDACO are directly compared to results by a recent study of state-of-the-art deterministic MINLP software on the same test set. Further comparisons with an established MINLP software is undertaken in addition. This study shows that MIDACO is not only competitive to the established MINLP software, but can even outperform those in terms of the number of global optimal solutions found. Moreover, the parallelization capabilities of MIDACO enable it to be even competitive to deterministic software regarding the amount of (serial processed) function evaluation, while the black-box capabilities of MIDACO offer an intriguing new robustness for MINLP.

Extensions of the Kuhn--Tucker Constraint Qualification to Generalized Semi-infinite Programming

This paper deals with the class of generalized semi-infinite programming problems (GSIPs) in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be continuously differentiable. We introduce two extensions of the Kuhn--Tucker constraint qualification (which is based on the existence of a tangential continuously differentiable arc) to the class of GSIPs, prove a corresponding Karush--Kuhn--Tucker theorem, and discuss its assumptions. Finally, we present several examples which illustrate for the class of GSIPs some interrelations between the considered extensions of the Mangasarian--Fromovitz constraint qualification, the Abadie constraint qualification, and the Kuhn--Tucker constraint qualification.

Augmented Lagrangians in semi-infinite programming

We consider the class of semi-infinite programming problems which became in recent years a powerful tool for the mathematical modeling of many real-life problems. In this paper, we study an augmented Lagrangian approach to semi-infinite problems and present necessary and sufficient conditions for the existence of corresponding augmented Lagrange multipliers. Furthermore, we discuss two particular cases for the augmenting function: the proximal Lagrangian and the sharp Lagrangian.

On Proper Efficiency in Multiobjective Semi-infinite Optimization

This chapter deals with multiobjective semi-infinite optimization problems which are defined by finitely many objective functions and infinitely many inequality constraints in a finite-dimensional space. We discuss constraint qualifications as well as necessary and sufficient conditions for locally weakly efficient solutions. Furthermore, we generalize two concepts of properly efficient solutions to the semi-infinite setting and present corresponding optimality conditions.

On saddle points in nonconvex semi-infinite programming

In this paper we apply two convexification procedures to the Lagrangian of a nonconvex semi-infinite programming problem. Under the reduction approach it is shown that, locally around a local minimizer, this problem can be transformed equivalently in such a way that the transformed Lagrangian fulfills saddle point optimality conditions, where for the first procedure both the original objective function and constraints (and for the second procedure only the constraints) are substituted by their pth powers with sufficiently large power p. These results allow that local duality theory and corresponding numerical methods (e.g. dual search) can be applied to a broader class of nonconvex problems.

On Interior Logarithmic Smoothing and Strongly Stable Stationary Points

The paper deals with a nonlinear programming problem (P) and, by using a logarithmic barrier function, a parametric family of interior point approximations

On Stable Feasible Sets in Generalized Semi-infinite Programming

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A note on strict complementarity for the doubly non-negative cone

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Surrogate-based model parameter optimization based on gas explosion experimental data

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On duality in multiobjective semi-infinite optimization

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