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O OBJAVOVANÍ A KONŠTRUOVANÍ MOŽNOSTÍ

100%

Schmidt M.

nr 9

793 – 803

The aim of the paper is to argue that it is not possible to approach modalities solely on empiric grounds as the followers of Kripke and Putnam maintain. This holds even in the case of nomological possibilities that are rooted in the laws of nature. There are no laws of nature that prevent scenarios opposing reality, for instance, no law precludes the possibility of the evening star not being identical with the morning star. As the paper argues, in order to prevent these scenarios, the concept of nomological possibility must contain some pieces of a priori metaphysics. Put differently, nomic possibilities are not just discovered, nomic possibilities are also construed.

TRACTARIAN OBJECTS IN THE STRUCTURAL SETTING

100%

Schmidt M.

tom 16

nr 3

328-343

The aim of the paper is to argue that the ontological setting of objects in Wittgenstein's 'Tractatus' is a version of structural realism. According to our plan, one of the opening statements of the Tractatus - The world is the totality of facts, not of things - introduces structuralist perspective: structures are superior to their constituents. However, structuralists use the notion 'superior' in various senses, but this paper argues that the Tractatus places its objects within the framework of ontic structural realism in its moderate form. That form puts structures and individuals on the same ontological footing. Such thesis contradicts traditional object-ontology that dominates Tractarian literature.

Convergence of finite-dimensional approximations for mixed-integer optimization with differential equations

63%

Hante F. M. , Schmidt M.

2019

tom Vol. 48, No. 2

209--226

We consider a direct approach to solving the mixedinteger nonlinear optimization problems with constraints depending on initial and terminal conditions of an ordinary differential equation. In order to obtain a finite-dimensional problem, the dynamics are approximated using discretization methods. In the framework of general one-step methods, we provide sufficient conditions for the convergence of this approach in the sense of the corresponding optimal values. The results are obtained by considering the discretized problem as a parametric mixed-integer nonlinear optimization problem in finite dimensions, where the step size for discretization of the dynamics is the parameter. In this setting, we prove the continuity of the optimal value function under a stability assumption for the integer feasible set and second-order conditions from nonlinear optimization. We address the necessity of the conditions on the example of pipe sizing problems for gas networks.

Time-domain decomposition for optimal control problems governed by semilinear hyperbolic systems with mixed two-point boundary conditions

45%

Krug R. , Leugering G. , Martin A. , Schmidt M. , Weninger D.

tom Vol. 50, No. 4

427--455

In this article, we study the time-domain decomposition of optimal control problems for systems of semilinear hyperbolic equations and provide an in-depth well-posedness analysis. This is a continuation of our work, Krug et al. (2021) in that we now consider mixed two-point boundary value problems. The more general boundary conditions significantly enlarge the scope of applications, e.g., to hyperbolic problems on metric graphs with cycles. We design an iterative method based on the optimality systems that can be interpreted as a decomposition method for the original optimal control problem into virtual control problems on smaller time domains.