Two-Level Optimization Problems with Infinite Number of Convex Lower Level Constraints

Bilevel Optimization with Nonsmooth Lower Level Problems

We consider a bilevel optimization approach for parameter learning in nonsmooth variational models. Existing approaches solve this problem by applying implicit differentiation to a sufficiently smooth approximation of the nondifferentiable lower level problem. We propose an alternative method based on differentiating the iterations of a nonlinear primal–dual algorithm. Our method computes exact...

Level-Set Topology Optimization with Aeroelastic Constraints

Level-set topology optimization is used to design a wing considering skin buckling under static aeroelastic trim loading, as well as dynamic aeroelastic stability (flutter). The level-set function is defined over the entire 3D volume of a transport aircraft wing box. Therefore, the approach is not limited by any predefined structure and can explore novel configurations. The Sequential Linear Pr...

SOLVING MULTI CONSTRAINTS STRUCTURAL TOPOLOGY OPTIMIZATION PROBLEM WITH REFORMULATION OF LEVEL SET METHOD

Due to the favorable performance of structural topology optimization to create a proper understanding in the early stages of design, this issue is taken into consideration from the standpoint of research or industrial application in recent decades. Over the last three decades, several methods have been proposed for topology optimization. One of the methods that has been effectively used in stru...

Separable convex optimization with nested lower and upper constraints

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified sampling, support vector machines, portfolio management, and telecommunications. We propose an efficient gradient-free divide-and-conquer algorithm, which use...

-Duality Theorems for Convex Semidefinite Optimization Problems with Conic Constraints

Efficient Convex Optimization for Minimal Partition Problems with Volume Constraints

Minimal partition problems describe the task of partitioning a domain into a set of meaningful regions. Two important examples are image segmentation and 3D reconstruction. They can both be formulated as energy minimization problems requiring minimum boundary length or surface area of the regions. This common prior often leads to the removal of thin or elongated structures. Volume constraints i...