Constrained Conjugate Gradient Algorithm Research Articles

Spectral Three-Term Constrained Conjugate Gradient Algorithm for Function Minimizations

In this work, we tend to deal within the field of the constrained optimization methods of three-term Conjugate Gradient (CG) technique which is primarily based on Dai–Liao (DL) formula. The new proposed technique satisfies the conjugacy property and the descent conditions of Karush–Kuhn–Tucker (K.K.T.). Our planned constrained technique uses the robust Wolfe line search condition with some assumptions. We tend to prove the global convergence property of the new planned technique. Numeral comparisons for (30-thirty) constrained optimization issues make sure the effectiveness of the new planned formula.

Performance evaluation of pulsed photothermal profiling of port wine stain in human skin

Treatment of port wine stain (PWS) birthmarks in human skin by pulsed laser irradiation requires the knowledge of the maximum epidermal temperature rise and PWS depth for an attending physician to select the optimal light dosage, irradiation wavelength, and cryogen spray cooling spurt duration on an individual patient basis. Pulsed photothermal radiometry (PPTR) is a promising technique to provide such information. In this article, computer simulations are performed to evaluate the performance of PPTR depth profiling of the laser-induced temperature rise in PWS. An iterative, non-negatively constrained conjugate gradient algorithm is used to reconstruct the laser-induced temperature profile from simulated PPTR signals. Human skin is assumed to contain an epidermal melanin layer and a single homogeneous PWS layer in the dermis. The influence of structural, experimental, and algorithm parameters on the temperature profile reconstruction are discussed. Accuracy of the maximum epidermal temperature rise and PWS depth determined from the reconstructed profiles is statistically analyzed. The simulations show that when the melanin and PWS layers are physically discrete, a good reconstruction can be obtained and the maximum epidermal temperature rise and PWS depth can be determined with accuracy sufficient for the intended clinical application. Measurements and reconstructions from PWS patients are performed and the results are in agreement with the simulations.

Accuracy of subsurface temperature distributions computed from pulsed photothermal radiometry

Pulsed photothermal radiometry (PPTR) is a non-contact method for determining the temperature increase in subsurface chromophore layers immediately following pulsed laser irradiation. In this paper the inherent limitations of PPTR are identified. A time record of infrared emission from a test material due to laser heating of a subsurface chromophore layer is calculated and used as input data for a non-negatively constrained conjugate gradient algorithm. Position and magnitude of temperature increase in a model chromophore layer immediately following pulsed laser irradiation are computed. Differences between simulated and computed temperature increase are reported as a function of thickness, depth and signal-to-noise ratio (SNR). The average depth of the chromophore layer and integral of temperature increase in the test material are accurately predicted by the algorithm. When the thickness/depth ratio is less than 25%, the computed peak temperature increase is always significantly less than the true value. Moreover, the computed thickness of the chromophore layer is much larger than the true value. The accuracy of the computed subsurface temperature distribution is investigated with the singular value decomposition of the kernel matrix. The relatively small number of right singular vectors that may be used (8% of the rank of the kernel matrix) to represent the simulated temperature increase in the test material limits the accuracy of PPTR. We show that relative error between simulated and computed temperature increase is essentially constant for a particular thickness/depth ratio.

Imaging laser heated subsurface chromophores in biological materials: determination of lateral physical dimensions

We describe a non-contact method using infrared radiometry to determine lateral physical dimensions of laser heated subsurface chromophores in biological materials. An imaging equation is derived that relates measured radiometric temperature change to the reduced two-dimensional temperature increase of laser heated chromophores. From measured images of radiometric temperature change, the lateral physical dimensions of chromophores positioned in an in vitro model of human skin are determined by deconvolution of the derived imaging equation using a non-negative constrained conjugate gradient algorithm. Conditions for optimum spatial resolution are found by analysis of a derived radiometric transfer function and correspond to superficial chromophores and/or weak infrared absorption in a laser irradiated biological material. Analysis indicates that if the infrared attenuation coefficient is sufficiently small (i.e., less than 10 ), infrared radiometry in combination with a deconvolution algorithm allows estimation of lateral physical dimensions of laser heated subsurface chromophores in human skin.

Control system design using frequency domain models and parameter optimization with application to supersonic inlet controls : Seidel, R. C. and Lehtinen, B. NASA Technical Memorandum, NSA TM X-3108 (October 1974) p.49

A technique is described for designing feedback control systems using frequency domain models, a quadratic cost function, and a parameter optimization computer program. FORTRAN listings for the computer program are included. The approach is applied to the design of shock position controllers for a supersonic inlet. Deterministic or random system disturbances, and the presence of random measurement noise are considered. The cost function minimization is formulated in the time domain, but the problem solution is obtained using a frequency domain system description. A scaled and constrained conjugate gradient algorithm is used for the minimization. The approach to a supersonic inlet included the calculations of the optimal proportional-plus integral (PI) and proportional-plus-integral-plus-derivative controllers. A single-loop PI controller was the most desirable of the designs considered.