A sequential semidefinite programming method and an application in passive reduced-order modeling

We consider the solution of nonlinear programs with nonlinear semidefiniteness constraints. The need for an efficient exploitation of the cone of positive semidefinite matrices makes the solution of such nonlinear semidefinite programs more complicated than the solution of standard nonlinear programs. In particular, a suitable symmetrization procedure needs to be chosen for the linearization of the complementarity condition. The choice of the symmetrization procedure can be shifted in a very natural way to certain linear semidefinite subproblems, and can thus be reduced to a well-studied problem. The resulting sequential semidefinite programming (SSP) method is a generalization of the well-known SQP method for standard nonlinear programs. We present a sensitivity result for nonlinear semidefinite programs, and then based on this result, we give a self-contained proof of local quadratic convergence of the SSP method. We also describe a class of nonlinear semidefinite programs that arise in passive reduced-order modeling, and we report results of some numerical experiments with the SSP method applied to problems in that class

Truss geometry and topology optimization with global stability constraints

In this paper, we introduce geometry optimization into an existing topology optimization workflow for truss structures with global stability constraints, assuming a linear buckling analysis. The design variables are the cross-sectional areas of the bars and the coordinates of the joints. This makes the optimization problem formulations highly nonlinear and yields nonconvex semidefinite programming problems, for which there are limited available numerical solvers compared with other classes of optimization problems. We present problem instances of truss geometry and topology optimization with global stability constraints solved using a standard primal-dual interior point implementation. During the solution process, both the cross-sectional areas of the bars and the coordinates of the joints are concurrently optimized. Additionally, we apply adaptive optimization techniques to allow the joints to navigate larger move limits and to improve the quality of the optimal designs

Egg production of Baltic cod (Gadus morhua) in relation to variable sex ratio, maturity, and fecundity

Observed fluctuations in relative fecundity of Eastern Baltic cod (Gadus morhua L.) were related to food availability during the main feeding period and were used to develop a predictive model that explained 72% of the interannual variations in fecundity. Time series of sex ratios, maturity ogives, and relative fecundity were combined with mean weights-at-age and stock sizes from an analytical multispecies model to estimate the potential egg production (PEP). Relationships between PEP and independent estimates of realized daily and seasonal egg production from egg surveys were highly significant. The difference between estimates of potential and realized seasonal egg production was of a magnitude corresponding to the expected loss of eggs as a result of atresia, fertilization failure, and early egg mortality. The removal of interannual variability in sex ratio, maturity, and fecundity on estimates of PEP deteriorated the relationships in all three cases. PEP proved to be superior to spawning stock biomass as measure of the reproductive potential in a stock-recruitment relationship of Eastern Baltic cod. PEP in combination with the reproductive volume explained 61% of the variation in year-class strength at age 2

A QMR-based interior-point algorithm for solving linear programs

A new approach for the implementation of interior-point methods for solving linear programs is proposed. Its main feature is the iterative solution of the symmetric, but highly indefinite 2 × 2-block systems of linear equations that arise within the interior-point algorithm. These linear systems are solved by a symmetric variant of the quasi-minimal residual (QMR) algorithm, which is an iterative solver for general linear systems. The symmetric QMR algorithm can be combined with indefinite preconditioners, which is crucial for the efficient solution of highly indefinite linear systems, yet it still fully exploits the symmetry of the linear systems to be solved. To support the use of the symmetric QMR iteration, a novel stable reduction of the original unsymmetric 3 × 3-block systems to symmetric 2 × 2-block systems is introduced, and a measure for a low relative accuracy for the solution of these linear systems within the interior-point algorithm is proposed. Some indefinite preconditioners are discussed. Finally, we report results of a few preliminary numerical experiments to illustrate the features of the new approach

Synthese und reaktionen von symmetrisch substituierten s-Triazinen unter hohem druck. Hochdruckreaktionen, 8. Mitteilung.

Two extensive mechanisms are proposed for cyclotrimerization of nitriles to s-triazines under high pressure. The availability of these mechanisms is proven by synthesis of some new symmetrically substituted s-triazines; simultaneously, however, their limits are demonstrated. Furthermore, there were found rearrangement and cyclic degradation reactions as reaction possibilities for s-triazines under high pressure. Both reactions are based on an equilibrium in alcohol between symmetrically substituted s-triazine and iminoether