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The remarkable generative capabilities of multimodal foundation models are currently being explored for a variety of applications. Generating radiological impressions is a challenging task that could significantly reduce the workload of radiologists. In our study we explored and analyzed the generative abilities of GPT-4 for Chest X-ray impression generation. To generate and evaluate impressions of chest X-rays based on different input modalities (image, text, text and image), a blinded radiological report was written for 25-cases of the publicly available NIH-dataset. GPT-4 was given image, finding section or both sequentially to generate an input dependent impression. In a blind randomized reading, 4-radiologists rated the impressions and were asked to classify the impression origin (Human, AI), providing justification for their decision. Lastly text model evaluation metrics and their correlation with the radiological score (summation of the 4 dimensions) was assessed. According to the radiological score, the human-written impression was rated highest, although not significantly different to text-based impressions. The automated evaluation metrics showed moderate to substantial correlations to the radiological score for the image impressions, however individual scores were highly divergent among inputs, indicating insufficient representation of radiological quality. Detection of AI-generated impressions varied by input and was 61% for text-based impressions. Impressions classified as AI-generated had significantly worse radiological scores even when written by a radiologist, indicating potential bias. Our study revealed significant discrepancies between a radiological assessment and common automatic evaluation metrics depending on the model input. The detection of AI-generated findings is subject to bias that highly rated impressions are perceived as human-written.

In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control problems with control constraints where the reference control plays the role of the parameter and has to be reconstructed. First, it is shown that pointwise M-stationarity, associated with the reformulation of the hierarchical model as a so-called mathematical problem with complementarity constraints (MPCC) in function spaces, provides a necessary optimality condition under some additional assumptions on the data. Second, we review two recently developed algorithms (an augmented Lagrangian method and a nonsmooth Newton method) for the computational identification of M-stationary points of finite-dimensional MPCCs. Finally, a numerical comparison of these methods, based on instances of the appropriately discretized inverse optimal control problem of our interest, is provided., Comment: 31 pages, 4 tables

We present a method to solve a special class of parameter identification problems for an elliptic optimal control problem to global optimality. The bilevel problem is reformulated via the optimal-value function of the lower-level problem. The reformulated problem is nonconvex and standard regularity conditions like Robinson's CQ are violated. Via a relaxation of the constraints, the problem can be decomposed into a family of convex problems and this is the basis for a solution algorithm. The convergence properties are analyzed. It is shown that a penalty method can be employed to solve this family of problems while maintaining convergence speed. For an example problem, the use of the identity as penalty function allows for the solution by a semismooth Newton method. Numerical results are presented. Difficulties and limitations of our approach to solve a nonconvex problem to global optimality are discussed.

We show that an optimality condition of M-stationarity type holds for minimizers of a class of mathematical programs with complementarity constraints (MPCCs) in Lebesgue spaces. We apply these results also to local minimizers of an inverse optimal control problem (which is an instance of an infinite-dimensional bilevel optimization problem). The multipliers for the M-stationarity system can be constructed via convex combinations of various multipliers to auxiliary, linear problems. However, proving the existence of the multipliers to these auxiliary problems is difficult and only possible in some situations., Comment: 35 pages

We introduce new first-order necessary conditions for mathematical programs with complementarity constraints (MPCCs), which lie between strong and M-stationarity and have a relatively simple description. We show that they hold for local minimizers under the rather weak constraint qualification MPCC-GCQ. As a generalization, we also get a class of stationarity conditions that lie between strong and C-stationarity and show that they also hold for local minimizers under MPCC-GCQ. We also present similar results for mathematical programs with vanishing constraints (MPVCs), and a very simple and elementary proof of M-stationarity for local minimizers of MPVCs.

It is known in the literature that local minimizers of mathematical programs with complementarity constraints (MPCCs) are so-called M-stationary points, if a weak MPCC-tailored Guignard constraint qualification (called MPCC-GCQ) holds. In this paper we present a new elementary proof for this result. Our proof is significantly simpler than existing proofs and does not rely on deeper technical theory such as calculus rules for limiting normal cones. A crucial ingredient is a proof of a (to the best of our knowledge previously open) conjecture, which was formulated in a Diploma thesis by Schinabeck., Comment: 7 pages

We show that the Mordukhovich-stationarity system associated with a mathematical program with complementarity constraints (MPCC) can be equivalently written as a system of discontinuous equations which can be tackled with a semismooth Newton method. We show that the resulting algorithm can be interpreted as an active set strategy for MPCCs. Local fast convergence of the method is guaranteed under validity of an MPCC-tailored version of LICQ and a suitable second-order condition. In case of linear-quadratic MPCCs, the LICQ-type constraint qualification can be replaced by a weaker condition which depends on the underlying multipliers. We discuss a suitable globalization strategy for our method. Some numerical results are presented in order to illustrate our theoretical findings.