The MM Alternative to EM

The EM algorithm is a special case of a more general algorithm called the MM algorithm. Specific MM algorithms often have nothing to do with missing data. The first M step of an MM algorithm creates a surrogate function that is optimized in the second M step. In minimization, MM stands for majorize--minimize; in maximization, it stands for minorize--maximize. This two-step process always drives the objective function in the right direction. Construction of MM algorithms relies on recognizing and manipulating inequalities rather than calculating conditional expectations. This survey walks the reader through the construction of several specific MM algorithms. The potential of the MM algorithm in solving high-dimensional optimization and estimation problems is its most attractive feature. Our applications to random graph models, discriminant analysis and image restoration showcase this ability.Comment: Published in at http://dx.doi.org/10.1214/08-STS264 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Multiscale, thermomechanical topology optimization of self-supporting cellular structures for porous injection molds

Purpose This paper aims to establish a multiscale topology optimization method for the optimal design of non-periodic, self-supporting cellular structures subjected to thermo-mechanical loads. The result is a hierarchically complex design that is thermally efficient, mechanically stable and suitable for additive manufacturing (AM). Design/methodology/approach The proposed method seeks to maximize thermo-mechanical performance at the macroscale in a conceptual design while obtaining maximum shear modulus for each unit cell at the mesoscale. Then, the macroscale performance is re-estimated, and the mesoscale design is updated until the macroscale performance is satisfied. Findings A two-dimensional Messerschmitt Bolkow Bolhm (MBB) beam withstanding thermo-mechanical load is presented to illustrate the proposed design method. Furthermore, the method is implemented to optimize a three-dimensional injection mold, which is successfully prototyped using 420 stainless steel infiltrated with bronze. Originality/value By developing a computationally efficient and manufacturing friendly inverse homogenization approach, the novel multiscale design could generate porous molds which can save up to 30 per cent material compared to their solid counterpart without decreasing thermo-mechanical performance. Practical implications This study is a useful tool for the designer in molding industries to reduce the cost of the injection mold and take full advantage of AM

Design for Additive Manufacturing of Conformal Cooling Channels Using Thermal-Fluid Topology Optimization and Application in Injection Molds

Additive manufacturing allows the fabrication parts and tools of high complexity. This capability challenges traditional guidelines in the design of conformal cooling systems in heat exchangers, injection molds, and other parts and tools. Innovative design methods, such as network-based approaches, lattice structures, and structural topology optimization have been used to generate complex and highly efficient cooling systems; however, methods that incorporate coupled thermal and fluid analysis remain scarce. This paper introduces a coupled thermal-fluid topology optimization algorithm for the design of conformal cooling channels. With this method, the channel position problem is replaced to a material distribution problem. The material distribution directly depends on the effect of flow resistance, heat conduction, as well as forced and natural convection. The problem is formulated based on a coupling of Navier-Stokes equations and convection-diffusion equation. The problem is solved by gradient-based optimization after analytical sensitivity derived using the adjoint method. The algorithm leads a two -dimensional conceptual design having optimal heat transfer and balanced flow. The conceptual design is converted to three-dimensional channels and mapped to a morphological surface conformal to the injected part. The method is applied to design an optimal conformal cooling for a real three dimensional injection mold. The feasibility of the final designs is verified through simulations. The final designs can be exported as both three-dimensional graphic and surface mesh CAD format, bringing the manufacture department the convenience to run the tool path for final fitting

Coordinate descent algorithms for lasso penalized regression

Imposition of a lasso penalty shrinks parameter estimates toward zero and performs continuous model selection. Lasso penalized regression is capable of handling linear regression problems where the number of predictors far exceeds the number of cases. This paper tests two exceptionally fast algorithms for estimating regression coefficients with a lasso penalty. The previously known $\ell_2$ algorithm is based on cyclic coordinate descent. Our new $\ell_1$ algorithm is based on greedy coordinate descent and Edgeworth's algorithm for ordinary $\ell_1$ regression. Each algorithm relies on a tuning constant that can be chosen by cross-validation. In some regression problems it is natural to group parameters and penalize parameters group by group rather than separately. If the group penalty is proportional to the Euclidean norm of the parameters of the group, then it is possible to majorize the norm and reduce parameter estimation to $\ell_2$ regression with a lasso penalty. Thus, the existing algorithm can be extended to novel settings. Each of the algorithms discussed is tested via either simulated or real data or both. The Appendix proves that a greedy form of the $\ell_2$ algorithm converges to the minimum value of the objective function.Comment: Published in at http://dx.doi.org/10.1214/07-AOAS147 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Inject Printing Perovskite LED On Paper Substrate

This poster describes the process and results of inject printing a four-layer perovskite LED on a paper substrate