Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.

Uniform hierarchical MFI nanosheets prepared via anisotropic etching for solution-based sub–100-nm-thick oriented MFI layer fabrication

Zeolite nanosheets have shown unprecedented opportunities for a wide range of applications, yet developing facile methods for fabrication of uniform zeolite nanosheets remains a great challenge. Here, a facile approach involving anisotropic etching with an aqueous solution of tetrapropylammonium hydroxide (TPAOH) was developed for preparing uniform high–aspect ratio hierarchical MFI nanosheets. In addition, the mechanism associated with the formation of MFI nanosheets was proposed. In the next step, a dynamic air-liquid interface–assisted self-assembly method and single-mode microwave heating were used for b-oriented MFI nanosheets monolayer deposition and controlled in-plane solution-based epitaxial growth, respectively, ensuring the formation of well-intergrown b-oriented MFI layers with sub–100-nm thickness. Moreover, our study indicated that b-oriented ultrathin MFI layers could be fabricated on diverse substrates demonstrating excellent anticorrosion capacity, ionic sieving properties, and n-/i-butane isomer separation performance.

The stress field of Vrancea region from fault plane solution (FPS)

The fault plane solutions (FPS) of 247 seismic events were used for stress field investigation of the region. The eigenvectors t, p, b, and moment tensor M components for each FPS were defined and computed numerically. The obtained results confirm the hypothesis of subduction-type intermediate depth earthquakes for the Vrancea seismic region and this may be considered the first approximation of the stress field for the whole of the Vrancea (intermediate depth) region.