scholarly journals A primal barrier function Phase I algorithm for nonsymmetric conic optimization problems

2012 ◽  
Vol 29 (3) ◽  
pp. 499-517 ◽  
Author(s):  
Yasuaki Matsukawa ◽  
Akiko Yoshise
Keyword(s):  
Phase I ◽  
Barrier Function ◽  
Optimization Problems ◽  
Conic Optimization

scholarly journals Alfonso: Matlab Package for Nonsymmetric Conic Optimization

2021 ◽  
Author(s):  
Dávid Papp ◽  
Sercan Yıldız
Keyword(s):  
Barrier Function ◽  
Optimization Problems ◽  
Symmetric Cone ◽  
Conic Optimization ◽  
Iteration Complexity ◽  
Worst Case ◽  
Optimization Software ◽  
Second Order Cone ◽  
Matlab Package ◽  
Hyperbolicity Cones

We present alfonso, an open-source Matlab package for solving conic optimization problems over nonsymmetric convex cones. The implementation is based on the authors’ corrected analysis of a method of Skajaa and Ye. It enables optimization over any convex cone as long as a logarithmically homogeneous self-concordant barrier is available for the cone or its dual. This includes many nonsymmetric cones, for example, hyperbolicity cones and their duals (such as sum-of-squares cones), semidefinite and second-order cone representable cones, power cones, and the exponential cone. Besides enabling the solution of problems that cannot be cast as optimization problems over a symmetric cone, algorithms for nonsymmetric conic optimization also offer performance advantages for problems whose symmetric cone programming representation requires a large number of auxiliary variables or has a special structure that can be exploited in the barrier computation. The worst-case iteration complexity of alfonso is the best known for nonsymmetric cone optimization: [Formula: see text] iterations to reach an ε-optimal solution, where ν is the barrier parameter of the barrier function used in the optimization. Alfonso can be interfaced with a Matlab function (supplied by the user) that computes the Hessian of a barrier function for the cone. A simplified interface is also available to optimize over the direct product of cones for which a barrier function has already been built into the software. This interface can be easily extended to include new cones. Both interfaces are illustrated by solving linear programs. The oracle interface and the efficiency of alfonso are also demonstrated using an optimal design of experiments problem in which the tailored barrier computation greatly decreases the solution time compared with using state-of-the-art, off-the-shelf conic optimization software. Summary of Contribution: The paper describes an open-source Matlab package for optimization over nonsymmetric cones. A particularly important feature of this software is that, unlike other conic optimization software, it enables optimization over any convex cone as long as a suitable barrier function is available for the cone or its dual, not limiting the user to a small number of specific cones. Nonsymmetric cones for which such barriers are already known include, for example, hyperbolicity cones and their duals (such as sum-of-squares cones), semidefinite and second-order cone representable cones, power cones, and the exponential cone. Thus, the scope of this software is far larger than most current conic optimization software. This does not come at the price of efficiency, as the worst-case iteration complexity of our algorithm matches the iteration complexity of the most successful interior-point methods for symmetric cones. Besides enabling the solution of problems that cannot be cast as optimization problems over a symmetric cone, our software can also offer performance advantages for problems whose symmetric cone programming representation requires a large number of auxiliary variables or has a special structure that can be exploited in the barrier computation. This is also demonstrated in this paper via an example in which our code significantly outperforms Mosek 9 and SCS 2.

scholarly journals Safety of a formulation containing chitosan microparticles with chamomile: blind controlled clinical trial

2018 ◽  
Vol 26 (0) ◽  
Author(s):  
Danielle Cristina Garbuio ◽  
Cristina Mara Zamarioli ◽  
Maísa Oliveira de Melo ◽  
Patrícia Maria Berardo Gonçalves Maia Campos ◽  
Emília Campos de Carvalho ◽  
...  
Keyword(s):  
Clinical Trial ◽  
Clinical Trials ◽  
Single Dose ◽  
Phase I ◽  
Water Loss ◽  
Barrier Function ◽  
Transepidermal Water Loss ◽  
Controlled Clinical Trial ◽  
Topical Formulation ◽  
Healthy Participants

ABSTRACT Objective: to evaluate the safety of a topical formulation containing chamomile microparticles coated with chitosan in the skin of healthy participants. Method: phase I blind, controlled, non-randomized, single-dose clinical trial with control for skin, base formulation, and formulation with microparticles. The variables analyzed were irritation and hydration by the Wilcoxon and Kruskall-Wallis tests. Results: the study started with 35 participants with a mean age of 26.3 years. Of these, 30 (85.71%) were female, 29 (82.90%) were white skinned and 32 (91.40%) had no previous pathologies. One participant was removed from the study reporting erythema at the site of application, and four other participants for not attending the last evaluation. In the 30 participants who completed the study, the tested formulation did not cause erythema, peeling, burning, pruritus or pain; there was an improvement in cutaneous hydration in the site of application of the formulation with microparticles. In the evaluation of the barrier function, there was an increase in transepidermal water loss in all sites. Conclusion: the formulation with chamomile microparticles is safe for topical use, not causing irritation and improving skin hydration over four weeks of use. Its effects on barrier function need further investigation. No. RBR-3h78kz in the Brazilian Registry of Clinical Trials (ReBEC).

An Efficient Kriging-Based Constrained Optimization Algorithm by Global and Local Sampling in Feasible Region

2019 ◽  
Vol 142 (5) ◽  
Author(s):  
Tianzeng Tao ◽  
Guozhong Zhao ◽  
Shanhong Ren
Keyword(s):  
Phase I ◽  
Constrained Optimization ◽  
Objective Function ◽  
Optimization Design ◽  
Optimization Problems ◽  
Phase Iii ◽  
Benchmark Problems ◽  
Feasible Region ◽  
Sample Points ◽  
Local Sampling

Abstract To solve challenging optimization problems with time-consuming objective and constraints, a novel efficient Kriging-based constrained optimization (EKCO) algorithm is proposed in this paper. The EKCO mainly consists of three sampling phases. In phase I of EKCO, considering the significance of constraints, feasible region is constructed via employing a feasible region sampling (FRS) criterion. The FRS criterion can avoid the local clustering phenomenon of sample points. Therefore, phase I is also a global sampling process for the objective function in the feasible region. However, the objective function may be higher-order nonlinear than constraints. In phase II, by maximizing the prediction variance of the surrogate objective, more accurate objective function in the feasible region can be obtained. After global sampling, to accelerate the convergence of EKCO, an objective local sampling criterion is introduced in phase III. The verification of the EKCO algorithm is examined on 18 benchmark problems by several recently published surrogate-based optimization algorithms. The results indicate that the sampling efficiency of EKCO is higher than or comparable with that of the recently published algorithms while maintaining the high accuracy of the optimal solution, and the adaptive ability of the proposed algorithm also be validated. To verify the ability of EKCO to solve practical engineering problems, an optimization design problem of aeronautical structure is presented. The result indicates EKCO can find a better feasible design than the initial design with limited sample points, which demonstrates practicality of EKCO.

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