scholarly journals An Approximate Proximal Bundle Method to Minimize a Class of Maximum Eigenvalue Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Wei Wang ◽  
Lingling Zhang ◽  
Miao Chen ◽  
Sida Lin
Keyword(s):  
Objective Function ◽  
Optimal Solution ◽  
Cutting Plane ◽  
Bundle Method ◽  
Maximum Eigenvalue ◽  
Plane Model ◽  
Essential Idea ◽  
Proximal Bundle Method ◽  
The Difference ◽  
And Function

We present an approximate nonsmooth algorithm to solve a minimization problem, in which the objective function is the sum of a maximum eigenvalue function of matrices and a convex function. The essential idea to solve the optimization problem in this paper is similar to the thought of proximal bundle method, but the difference is that we choose approximate subgradient and function value to construct approximate cutting-plane model to solve the above mentioned problem. An important advantage of the approximate cutting-plane model for objective function is that it is more stable than cutting-plane model. In addition, the approximate proximal bundle method algorithm can be given. Furthermore, the sequences generated by the algorithm converge to the optimal solution of the original problem.

scholarly journals A Cutting Plane and Level Stabilization Bundle Method with Inexact Data for Minimizing Nonsmooth Nonconvex Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Jie Shen ◽  
Dan Li ◽  
Li-Ping Pang
Keyword(s):  
Objective Function ◽  
Cutting Plane ◽  
Bundle Method ◽  
Approximation Model ◽  
Nonconvex Functions ◽  
Proximal Bundle Methods ◽  
New Variant ◽  
Optimal Value ◽  
Inexact Data ◽  
Optimality Gap

Under the condition that the values of the objective function and its subgradient are computed approximately, we introduce a cutting plane and level bundle method for minimizing nonsmooth nonconvex functions by combining cutting plane method with the ideas of proximity control and level constraint. The proposed algorithm is based on the construction of both a lower and an upper polyhedral approximation model to the objective function and calculates new iteration points by solving a subproblem in which the model is employed not only in the objective function but also in the constraints. Compared with other proximal bundle methods, the new variant updates the lower bound of the optimal value, providing an additional useful stopping test based on the optimality gap. Another merit is that our algorithm makes a distinction between affine pieces that exhibit a convex or a concave behavior relative to the current iterate. Convergence to some kind of stationarity point is proved under some looser conditions.

A Redistributed Bundle Algorithm Based on Local Convexification Models for Nonlinear Nonsmooth DC Programming

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jie Shen ◽  
Na Xu ◽  
Fang-Fang Guo ◽  
Han-Yang Li ◽  
Pan Hu
Keyword(s):  
Cutting Plane ◽  
Dc Programming ◽  
Bundle Method ◽  
Difference Of Convex Functions ◽  
Bundle Algorithm ◽  
Difference Of Convex ◽  
Proximal Bundle Method ◽  
Local Convexification ◽  
Original Objective ◽  
Linearization Errors

Abstract For nonlinear nonsmooth DC programming (difference of convex functions), we introduce a new redistributed proximal bundle method. The subgradient information of both the DC components is gathered from some neighbourhood of the current stability center and it is used to build separately an approximation for each component in the DC representation. Especially we employ the nonlinear redistributed technique to model the second component of DC function by constructing a local convexification cutting plane. The corresponding convexification parameter is adjusted dynamically and is taken sufficiently large to make the ”augmented” linearization errors nonnegative. Based on above techniques we obtain a new convex cutting plane model of the original objective function. Based on this new approximation the redistributed proximal bundle method is designed and the convergence of the proposed algorithm to a Clarke stationary point is proved. A simple numerical experiment is given to show the validity of the presented algorithm.

scholarly journals An Adaptive Proximal Bundle Method with Inexact Oracles for a Class of Nonconvex and Nonsmooth Composite Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 874
Author(s):  
Xiaoliang Wang ◽  
Liping Pang ◽  
Qi Wu ◽  
Mingkun Zhang
Keyword(s):  
Convex Function ◽  
Cutting Plane ◽  
Bundle Method ◽  
Composite Optimization ◽  
Nonconvex Function ◽  
Inexact Information ◽  
Proximal Bundle Method ◽  
Approximate Function ◽  
Linearization Errors ◽  
Dc Problems

In this paper, an adaptive proximal bundle method is proposed for a class of nonconvex and nonsmooth composite problems with inexact information. The composite problems are the sum of a finite convex function with inexact information and a nonconvex function. For the nonconvex function, we design the convexification technique and ensure the linearization errors of its augment function to be nonnegative. Then, the sum of the convex function and the augment function is regarded as an approximate function to the primal problem. For the approximate function, we adopt a disaggregate strategy and regard the sum of cutting plane models of the convex function and the augment function as a cutting plane model for the approximate function. Then, we give the adaptive nonconvex proximal bundle method. Meanwhile, for the convex function with inexact information, we utilize the noise management strategy and update the proximal parameter to reduce the influence of inexact information. The method can obtain an approximate solution. Two polynomial functions and six DC problems are referred to in the numerical experiment. The preliminary numerical results show that our algorithm is effective and reliable.

Strategies for Oral Delivery of Metal-Saturated Lactoferrin

2019 ◽  
Vol 20 (11) ◽  
pp. 1046-1051 ◽  
Author(s):  
Przemysław Gajda-Morszewski ◽  
Klaudyna Śpiewak-Wojtyła ◽  
Maria Oszajca ◽  
Małgorzata Brindell
Keyword(s):  
Biological Activity ◽  
Oral Delivery ◽  
Therapeutic Potential ◽  
Structure And Function ◽  
The Difference ◽  
And Function ◽  
First Time

Lactoferrin was isolated and purified for the first time over 50-years ago. Since then, extensive studies on the structure and function of this protein have been performed and the research is still being continued. In this mini-review we focus on presenting recent scientific efforts towards the elucidation of the role and therapeutic potential of lactoferrin saturated with iron(III) or manganese(III) ions. The difference in biological activity of metal-saturated lactoferrin vs. the unmetalated one is emphasized. The strategies for oral delivery of lactoferrin, are also reviewed, with particular attention to the metalated protein.

scholarly journals Difference in patient-reported outcomes of various patellar component designs in total knee arthroplasty: A randomized clinical study

2021 ◽  
Vol 29 (1) ◽  
pp. 230949902199606
Author(s):  
Takeshi Mochizuki ◽  
Koichiro Yano ◽  
Katsunori Ikari ◽  
Ken Okazaki
Keyword(s):  
Knee Osteoarthritis ◽  
Clinical Effects ◽  
Patellar Component ◽  
American College Of Rheumatology ◽  
Randomized Clinical Study ◽  
Component Design ◽  
Patient Reported ◽  
Total Knee ◽  
The Difference ◽  
And Function

Purpose: This study investigated the clinical effects of different patellar components without being affected by the femoral component design in total knee arthritis (TKA) for patients with knee osteoarthritis (OA). Methods: In total, 48 patients with OA who met the criteria of the American College of Rheumatology for OA were enrolled and randomly assigned in a 1:1 ratio to two groups according to the usage of patellar component design for TKA (medialized dome type [dome group] or medialized anatomic type [anatomic group]). To evaluate the clinical outcomes for TKA, knee range of motion (ROM), pain intensity of 0–100 mm visual analog scale (pain VAS), and the Japanese Knee Osteoarthritis Measure (JKOM) score were obtained at baseline and year 1. Results: The difference in knee ROM, pain VAS, or total JKOM score at year 1 was not significant between the dome and anatomic groups ( p = 0.398, 0.733 and 0.536, respectively). Moreover, similar results were obtained for changes in knee ROM, pain VAS, or total JKOM scores from baseline. In both groups, the pain VAS and total JKOM scores were significantly improved at year 1. Conclusion: Both dome and anatomic groups in TKA are significantly effective for pain and function using the JKOM score. However, their efficacy did not differ, according to the JKOM score. Results of this study are rare information focusing on the patellar component design and provide one of the insights into the TKA clinical management.

scholarly journals Modeled 3D-Structures of Proteobacterial Transglycosylases from Glycoside Hydrolase Family 17 Give Insight in Ligand Interactions Explaining Differences in Transglycosylation Products

2021 ◽  
Vol 11 (9) ◽  
pp. 4048
Author(s):  
Javier A. Linares-Pastén ◽  
Lilja Björk Jonsdottir ◽  
Gudmundur O. Hreggvidsson ◽  
Olafur H. Fridjonsson ◽  
Hildegard Watzlawick ◽  
...  
Keyword(s):  
Glycoside Hydrolase ◽  
Ligand Docking ◽  
Glycoside Hydrolase Family ◽  
Ligand Interactions ◽  
Tim Barrel ◽  
Branching Point ◽  
The Difference ◽  
Dynamics Simulations ◽  
And Function ◽  
Hydrolase Family

The structures of glycoside hydrolase family 17 (GH17) catalytic modules from modular proteins in the ndvB loci in Pseudomonas aeruginosa (Glt1), P. putida (Glt3) and Bradyrhizobium diazoefficiens (previously B. japonicum) (Glt20) were modeled to shed light on reported differences between these homologous transglycosylases concerning substrate size, preferred cleavage site (from reducing end (Glt20: DP2 product) or non-reducing end (Glt1, Glt3: DP4 products)), branching (Glt20) and linkage formed (1,3-linkage in Glt1, Glt3 and 1,6-linkage in Glt20). Hybrid models were built and stability of the resulting TIM-barrel structures was supported by molecular dynamics simulations. Catalytic amino acids were identified by superimposition of GH17 structures, and function was verified by mutagenesis using Glt20 as template (i.e., E120 and E209). Ligand docking revealed six putative subsites (−4, −3, −2, −1, +1 and +2), and the conserved interacting residues suggest substrate binding in the same orientation in all three transglycosylases, despite release of the donor oligosaccharide product from either the reducing (Glt20) or non-reducing end (Glt1, Gl3). Subsites +1 and +2 are most conserved and the difference in release is likely due to changes in loop structures, leading to loss of hydrogen bonds in Glt20. Substrate docking in Glt20 indicate that presence of covalently bound donor in glycone subsites −4 to −1 creates space to accommodate acceptor oligosaccharide in alternative subsites in the catalytic cleft, promoting a branching point and formation of a 1,6-linkage. The minimum donor size of DP5, can be explained assuming preferred binding of DP4 substrates in subsite −4 to −1, preventing catalysis.

Effects of avertin versus xylazine-ketamine anesthesia on cardiac function in normal mice

2001 ◽  
Vol 281 (5) ◽  
pp. H1938-H1945 ◽  
Author(s):  
Chari Y. T. Hart ◽  
John C. Burnett ◽  
Margaret M. Redfield
Keyword(s):  
Cardiac Function ◽  
Diastolic Pressure ◽  
Systolic Function ◽  
Pressure Rise ◽  
Left Ventricular ◽  
Lv Function ◽  
Ketamine Anesthesia ◽  
The Difference ◽  
And Function ◽  
Derivatives Of

Anesthetic regimens commonly administered during studies that assess cardiac structure and function in mice are xylazine-ketamine (XK) and avertin (AV). While it is known that XK anesthesia produces more bradycardia in the mouse, the effects of XK and AV on cardiac function have not been compared. We anesthetized normal adult male Swiss Webster mice with XK or AV. Transthoracic echocardiography and closed-chest cardiac catheterization were performed to assess heart rate (HR), left ventricular (LV) dimensions at end diastole and end systole (LVDd and LVDs, respectively), fractional shortening (FS), LV end-diastolic pressure (LVEDP), the time constant of isovolumic relaxation (τ), and the first derivatives of LV pressure rise and fall (dP/d t max and dP/d t min, respectively). During echocardiography, HR was lower in XK than AV mice (250 ± 14 beats/min in XK vs. 453 ± 24 beats/min in AV, P < 0.05). Preload was increased in XK mice (LVDd: 4.1 ± 0.08 mm in XK vs. 3.8 ± 0.09 mm in AV, P < 0.05). FS, a load-dependent index of systolic function, was increased in XK mice (45 ± 1.2% in XK vs. 40 ± 0.8% in AV, P < 0.05). At LV catheterization, the difference in HR with AV (453 ± 24 beats/min) and XK (342 ± 30 beats/min, P < 0.05) anesthesia was more variable, and no significant differences in systolic or diastolic function were seen in the group as a whole. However, in XK mice with HR <300 beats/min, LVEDP was increased (28 ± 5 vs. 6.2 ± 2 mmHg in mice with HR >300 beats/min, P < 0.05), whereas systolic (LV dP/d t max: 4,402 ± 798 vs. 8,250 ± 415 mmHg/s in mice with HR >300 beats/min, P < 0.05) and diastolic (τ: 23 ± 2 vs. 14 ± 1 ms in mice with HR >300 beats/min, P < 0.05) function were impaired. Compared with AV, XK produces profound bradycardia with effects on loading conditions and ventricular function. The disparate findings at echocardiography and LV catheterization underscore the importance of comprehensive assessment of LV function in the mouse.

A Proximal Bundle Method with Exact Penalty Technique and Bundle Modification Strategy for Nonconvex Nonsmooth Constrained Optimization

2021 ◽  
pp. 2150015
Author(s):  
Xiaoliang Wang ◽  
Liping Pang ◽  
Qi Wu
Keyword(s):  
Operation Research ◽  
Bundle Method ◽  
Exact Penalty ◽  
Constraint Function ◽  
Modified Model ◽  
Proximal Bundle Method ◽  
Unconstrained Problem ◽  
Unconstrained Problems ◽  
Penalty Strategy ◽  
Penalty Technique

The bundle modification strategy for the convex unconstrained problems was proposed by Alexey et al. [[2007] European Journal of Operation Research, 180(1), 38–47.] whose most interesting feature was the reduction of the calls for the quadratic programming solver. In this paper, we extend the bundle modification strategy to a class of nonconvex nonsmooth constraint problems. Concretely, we adopt the convexification technique to the objective function and constraint function, take the penalty strategy to transfer the modified model into an unconstrained optimization and focus on the unconstrained problem with proximal bundle method and the bundle modification strategies. The global convergence of the corresponding algorithm is proved. The primal numerical results show that the proposed algorithms are promising and effective.

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