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The column-and-constraint generation (CCG) method was introduced by \citet{Zeng2013} for solving two-stage adaptive optimization. We found that the CCG method is quite scalable, but sometimes, and in some applications often, produces infeasible first-stage solutions, even though the problem is feasible. In this research, we extend the CCG method in a way that (a) maintains scalability and (b) always produces feasible first-stage decisions if they exist. We compare our method to several recently proposed methods and find that it reaches high accuracies faster and solves significantly larger problems.

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group., Comment: 28 pages, in 2 languages - English and Russian

In this paper we study convex bi-level optimization problems for which the inner level consists of minimization of the sum of smooth and nonsmooth functions. The outer level aims at minimizing a smooth and strongly convex function over the optimal solutions set of the inner problem. We analyze a first order method which is based on an existing fixed-point algorithm. Global sublinear rate of convergence of the method is established in terms of the inner objective function values.

Many shape analysis methods treat the geometry of an object as a metric space that can be captured by the Laplace-Beltrami operator. In this paper, we propose to adapt the classical Hamiltonian operator from quantum mechanics to the field of shape analysis. To this end we study the addition of a potential function to the Laplacian as a generator for dual spaces in which shape processing is performed. We present a general optimization approach for solving variational problems involving the basis defined by the Hamiltonian using perturbation theory for its eigenvectors. The suggested operator is shown to produce better functional spaces to operate with, as demonstrated on different shape analysis tasks.

Automatic estimation of skinning transformations is a popular way to deform a single reference shape into a new pose by providing a small number of control parameters. We generalize this approach by efficiently enabling the use of multiple exemplar shapes. Using a small set of representative natural poses, we propose to express an unseen appearance by a low-dimensional linear subspace, specified by a redundant dictionary of weighted vertex positions. Minimizing a nonlinear functional that regulates the example manifold, the suggested approach supports local-rigid deformations of articulated objects, as well as nearly isometric embeddings of smooth shapes. A real-time non-rigid deformation system is demonstrated, and a shape completion and partial registration framework is introduced. These applications can recover a target pose and implicit inverse kinematics from a small number of examples and just a few vertex positions. The result reconstruction is more accurate compared to state-of-the-art reduced deformable models.

Transparent Al2O3 ceramics have attracted considerable interest for use in a wide range of optical, electronic and structural applications. The fabrication of these ceramics using powder metallurgy processes requires the development of theoretical approaches to the compaction of nanopowders. In this work, we investigate the compaction processes of two model granular systems imitating Al2O3 nanosized powders. System I is a loosely aggregated powder, and system II is a powder strongly inclined to agglomeration (for instance, calcined powder). The processes of isostatical (uniform), biaxial, and uniaxial compaction as well as uniaxial compaction with simultaneous shear deformation are studied. The energy parameters of compaction such as the energy change of elastic interparticle interactions and dispersion interactions, dissipative energy losses related to the processes of interparticle friction, and the total work of compaction are calculated for all the processes. The nonapplicability of the associated flow rule to the description of deformation processes of oxide nanopowders is shown and an alternative plastic flow rule is suggested. A complete system of determining the relationship of the flow including analytical approximations of yield surfaces is obtained., Comment: 9 pages, 5 figures, 17 references

We consider the problem of minimizing a function, which is the sum of a linear function and a composition of a strongly convex function with a linear transformation, over a compact polyhedral set. Jaggi and Lacoste-Julien [14] showed that the conditional gradient method with away steps employed on the aforementioned problem without the additional linear term has linear rate of convergence, depending on the so-called pyramidal width of the feasible set. We revisit this result and provide a variant of the algorithm and an analysis that is based on simple duality arguments, as well as corresponding error bounds. This new analysis (a) enables the incorporation of the additional linear term, (b) does not require a linear-oracle that outputs an extreme point of the linear mapping of the feasible set and (c) depends on a new constant, termed "the vertex-facet distance constant", which is explicitly expressed in terms of the problem's parameters and the geometry of the feasible set. This constant replaces the pyramidal width, which is difficult to evaluate.

Two granular systems (I and II) corresponding oxide nanopowders having different agglomeration tendency are simulated by the granular dynamics method. The particle size is 10 nanometer. The interaction of particles involves the elastic forces of repulsion, the tangential forces of "friction", the dispersion forces of attraction, and in the case of II system the opportunity of creation/destruction of hard bonds of chemical nature. The processes of the uniaxial compaction, the biaxial (radial) one, the isotropic one, the compaction combined with shear deformation as well as the simple shear deformation are studied. The effect of the positive dilatancy is found out in the processes of shear deformation. The loading surfaces of nanopowders are constructed in the space of stress tensor invariants, i.e., the hydrostatic pressure and the deviator intensity. It is revealed that the form of the loading surfaces is similar to an ellipse, which is shifted along the hydrostatic axis to compressive pressures. The associated flow rule is analyzed. The nonorthogonality of the deformation vectors to the loading surface is established in the both systems modeled., Comment: 14 pages, 9 figures, 40 references