K-Optimal Design via Semidefinite Programming and Entropy Optimization

2015 ◽  
Vol 40 (2) ◽  
pp. 495-512 ◽  
Author(s):  
Pierre Maréchal ◽  
Jane J. Ye ◽  
Julie Zhou
Keyword(s):  
Optimal Design ◽  
Semidefinite Programming ◽  
Entropy Optimization

scholarly journals Optimal Design of Experiments for Liquid–Liquid Equilibria Characterization via Semidefinite Programming

Processes ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 834 ◽  
Author(s):  
Belmiro P.M. Duarte ◽  
Anthony C. Atkinson ◽  
José F.O. Granjo ◽  
Nuno M.C. Oliveira
Keyword(s):  
Optimal Design ◽  
Design Of Experiments ◽  
Semidefinite Programming ◽  
Information Matrix ◽  
Ternary Systems ◽  
Initial Mixture ◽  
Optimality Criteria ◽  
Optimal Design Of Experiments ◽  
Optimization Formulation ◽  
Considerable Work

Liquid–liquid equilibria (LLE) characterization is a task requiring considerable work and appreciable financial resources. Notable savings in time and effort can be achieved when the experimental plans use the methods of the optimal design of experiments that maximize the information obtained. To achieve this goal, a systematic optimization formulation based on Semidefinite Programming is proposed for finding optimal experimental designs for LLE studies carried out at constant pressure and temperature. The non-random two-liquid (NRTL) model is employed to represent species equilibria in both phases. This model, combined with mass balance relationships, provides a means of computing the sensitivities of the measurements to the parameters. To design the experiment, these sensitivities are calculated for a grid of candidate experiments in which initial mixture compositions are varied. The optimal design is found by maximizing criteria based on the Fisher Information Matrix (FIM). Three optimality criteria (D-, A- and E-optimal) are exemplified. The approach is demonstrated for two ternary systems where different sets of parameters are to be estimated.

Comparison of Semidefinite Solvers for Topology Optimization of Cantilever Trusses Subject to Fundamental Eigenvalue Constraint

2017 ◽  
Vol 1144 ◽  
pp. 172-177
Author(s):  
Marek Tyburec ◽  
Jan Zeman
Keyword(s):  
Topology Optimization ◽  
Optimal Design ◽  
Structural Optimization ◽  
Semidefinite Programming ◽  
Design Space ◽  
Model Problem ◽  
Free Vibrations ◽  
Ground Structure ◽  
Computational Performance ◽  
Structural Volume

Optimal design of trusses is a widely developed field of structural optimization. In topology optimization the infinite design space is usually discretized into a finite ground structure defining the set of all feasible joints and bars. In this paper we adopt semidefinite programming (SDP) formulation of the topology optimization that enables us to obtain a globally optimal least compliant truss subjected to the constraints on structural volume and on the fundamental eigenvalue of free vibrations. For a model problem of 3D cantilever truss, we present a comparison of six solvers, namely CSDP, MOSEK, PENLAB, SDPA, SDPT3 and SeDuMi, from which it follows, that SDPA delivers the best computational performance.

Crack divergence phenomena in tempered glass

2020 ◽  
Vol 13 (3) ◽  
pp. 115-129
Author(s):  
Shin’ichi Aratani
Keyword(s):  
Optimal Design ◽  
High Speed ◽  
Glass Plate ◽  
Acute Angle ◽  
Divergence Angle ◽  
High Speed Photography ◽  
Tempered Glass ◽  
Thick Glass

High speed photography using the Cranz-Schardin camera was performed to study the crack divergence and divergence angle in thermally tempered glass. A tempered 3.5 mm thick glass plate was used as a specimen. It was shown that two types of bifurcation and branching existed as the crack divergence. The divergence angle was smaller than the value calculated from the principle of optimal design and showed an acute angle.

G Optimal Design in Non linear Models to Increase Silicon Oxide Purity Levels and Electrical Conductivity

2018 ◽  
pp. 150-155
Author(s):  
Muklas Rivai
Keyword(s):  
Electrical Conductivity ◽  
Optimal Design ◽  
Linear Models ◽  
Silicon Oxide ◽  
Information Matrix ◽  
Relevant Information ◽  
Non Linear

Optimal design is a design which required in determining the points of variable factors that would be attempted to optimize the relevant information so that fulfilled the desired criteria. The optimal fulfillment criteria based on the information matrix of the selected model.

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