The roof dual bound for quadratic unconstrained binary optimization is the basis for several methods for efficiently computing the solution to many hard combinatorial problems. It works by constructing the tightest possible lower-bounding submodular function, and instead of minimizing the original objective function, the relaxation is minimized. However, for higher-order problems the technique ...

In this paper, we aim at minimizing the actuator torques of robots working on production lines by adding to the mechanism dynamic equilibrators based on nonlinear springs, that work in parallel with the joints. We propose a method to simultaneously optimize the trajectory of the robot and the force profiles of the nonlinear springs to minimize the actuator torques. First, we express the traject...

It is observed that around the optimum point of the motionestimation process the error criterion function is well modeled as aquadratic function with respect to the motion vector offsets. This locallyquadratic functional model decomposes the motion estimation optimiza-tion at subpixel resolutions into a two-stage pipelinable processes: full-search at full-pixel resolution an...

The anomaly detection and localization problem can be treated as a multiple hypotheses testing (MHT) problem in the Bayesian framework. The Bayesian test with the 0-1 loss function is a standard solution for this problem, but the alternative hypotheses have quite different importance in practice. The 0-1 loss function does not reflect this fact while the quadratic loss function is more appropri...

In the past, optimization of engineering specifications primarily included influence quality loss terms on product quality; however, in actual production practice, compensation quantity inevitably affects specifications. this paper, quadratic exponential and gain function was first supplemented, constructed under larger-the-better characteristic smaller-the-better characteristic; order to accur...

Support Vector Machines Regression (SVMR) is a learning technique where the goodness of fit is measured not by the usual quadratic loss function (the mean square error), but by a different loss function called the -Insensitive Loss Function (ILF), which is similar to loss functions used in the field of robust statistics. The quadratic loss function is well justified under the assumption of Gaus...

This paper presents a feedback adjustment rule for discrete-part manufacturing processes that experience errors at the setup operation which are not directly observable due to part-topart variability and measurement error. In contrast to previous work on setup adjustment, the off-target cost function of the process is not symmetric around its target. Two asymmetric cost functions – constant and...

It has long been customary to measure the adequacy of an estimator by the smallness of its mean squared error. The least squares estimators were studied by Gauss and by other authors later in the nineteenth century. A proof that the best unbiased estimator of a linear function of the means of a set of observed random variables is the least squares estimator was given by Markov [12], a modified ...