Projection methods in conic optimization

There exist efficient algorithms to project a point onto the intersection of a convex cone and an affine subspace. Those conic projections are in turn the work-horse of a range of algorithms in conic optimization, having a variety of applications in science, finance and engineering. This chapter reviews some of these algorithms, emphasizing the so-called regularization algorithms for linear conic optimization, and applications in polynomial optimization. This is a presentation of the material of several recent research articles; we aim here at clarifying the ideas, presenting them in a general framework, and pointing out important techniques

A comparison of delamination models: Modeling, properties, and applications

This contribution presents recent results in the modeling and the analysis of delamination problems. It addresses adhesive contact, brittle, and cohesive zone models both in a quasistatic and a viscous, dynamic setting for the bulk part. Also different evolution laws for the delaminating surface are discussed

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

Long-term monitoring of fish in a freshwater reservoir: Different ways of weighting complex spatial samples

Anthropogenic activities continue to pose the greatest challenges to freshwater ecosystems. Therefore, long-term monitoring is essential for the management and conservation of these resources. Monitoring programs for freshwater bodies often use a range of indicators, including biological elements such as fish. Existing European standard provides a depth-stratified gillnet sampling approach mainly in benthic habitats and at the deepest part of lakes to account for the uneven distribution of fish. However, the commonly used CEN (European Committee for Standardization) protocol does not weight sufficiently habitat volumes and underrepresent pelagic habitats to calculate whole-lake catch and biomass per unit effort (CPUE and BPUE, respectively). Extended European standard gillnet (4 larger mesh-sizes added in the geometric series) catch data collected over 18 years (2004–2021) in Římov Reservoir (Czech Republic) were used for a method comparison on indices for relative abundance and biomass of fish: CEN protocol without volume-weighting and two volume-weighted approaches. We also evaluated changes in species composition and trends in these fish population over time. Results indicated interannual changes in species composition, relative abundance, and biomass of fish community. The CEN protocol tended to put greater emphasis on benthic habitats which generally have larger CPUE and BPUE. Consequently, the two volume-weighting approaches produced lower estimates of the two parameters, with the exception of the most dominant pelagic bleak Alburnus alburnus (L.). All approaches consistently showed an increasing trend in whole-reservoir fish abundance and a decreasing trend in biomass over the study period. Following our assessment, we put forward the volume-weighting approach that considers the Volume of the depth Stratum (VOST) for weighting as the most realistic approximation of fish populations and therefore recommend its use