Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective function; convex or strongly convex objective and constraint; deterministic or randomized information about the objective and constraint. We hope that it is convenient for a reader to have all the methods for different settings in one place. Described methods are based on Mirror Descent algorithm and switching subgradient scheme. One of our focus is to propose, for the listed different settings, a Mirror Descent with adaptive stepsizes and adaptive stopping rule. This means that neither stepsize nor stopping rule require to know the Lipschitz constant of the objective or constraint. We also construct Mirror Descent for problems with objective function, which is not Lipschitz continuous, e.g. is a quadratic function. Besides that, we address the problem of recovering the solution of the dual problem

Arbidol: a broad-spectrum antiviral that inhibits acute and chronic HCV infection

Arbidol (ARB) is an antiviral compound that was originally proven effective for treatment of influenza and several other respiratory viral infections. The broad spectrum of ARB anti-viral activity led us to evaluate its effect on hepatitis C virus (HCV) infection and replication in cell culture. Long-term ARB treatment of Huh7 cells chronically replicating a genomic length genotype 1b replicon resulted in sustained reduction of viral RNA and protein expression, and eventually cured HCV infected cells. Pre-treatment of human hepatoma Huh7.5.1 cells with 15 μM ARB for 24 to 48 hours inhibited acute infection with JFH-1 virus by up to 1000-fold. The inhibitory effect of ARB on HCV was not due to generalized cytotoxicity, nor to augmentation of IFN antiviral signaling pathways, but involved impaired virus-mediated membrane fusion. ARB's affinity for membranes may inhibit several aspects of the HCV lifecycle that are membrane-dependent

Stopping Rules for Gradient Methods for Non-Convex Problems with Additive Noise in Gradient

We study the gradient method under the assumption that an additively inexact gradient is available for, generally speaking, non-convex problems. The non-convexity of the objective function, as well as the use of an inexactness specified gradient at iterations, can lead to various problems. For example, the trajectory of the gradient method may be far enough away from the starting point. On the other hand, the unbounded removal of the trajectory of the gradient method in the presence of noise can lead to the removal of the trajectory of the method from the desired exact solution. The results of investigating the behavior of the trajectory of the gradient method are obtained under the assumption of the inexactness of the gradient and the condition of gradient dominance. It is well known that such a condition is valid for many important non-convex problems. Moreover, it leads to good complexity guarantees for the gradient method. A rule of early stopping of the gradient method is proposed. Firstly, it guarantees achieving an acceptable quality of the exit point of the method in terms of the function. Secondly, the stopping rule ensures a fairly moderate distance of this point from the chosen initial position. In addition to the gradient method with a constant step, its variant with adaptive step size is also investigated in detail, which makes it possible to apply the developed technique in the case of an unknown Lipschitz constant for the gradient. Some computational experiments have been carried out which demonstrate effectiveness of the proposed stopping rule for the investigated gradient methods

On representations of the feasible set in convex optimization

We consider the convex optimization problem $\min \{f(x) : g_j(x)\leq 0, j=1,...,m\}$ where $f$ is convex, the feasible set K is convex and Slater's condition holds, but the functions $g_j$ are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minimizer. That is, the KKT optimality conditions are necessary and sufficient as in convex programming where one assumes that the $g_j$ are convex. So in convex optimization, and as far as one is concerned with KKT points, what really matters is the geometry of K and not so much its representation.Comment: to appear in Optimization Letter

Structural Optimization Using the Newton Modified Barrier Method

The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program

Synthesis of a PID-controller of a trim robust control system of an autonomous underwater vehicle

Autonomous underwater vehicles are often used for performing scientific, emergency or other types of missions under harsh conditions and environments, which can have non-stable, variable parameters. So, the problem of developing autonomous underwater vehicle motion control systems, capable of operating properly in random environments, is highly relevant. The paper is dedicated to the synthesis of a PID-controller of a trim robust control system, capable of keeping an underwater vehicle stable during a translation at different angles of attack. In order to synthesize the PID-controller, two problems were solved: a new method of synthesizing a robust controller was developed and a mathematical model of an underwater vehicle motion process was derived. The newly developed mathematical model structure is simpler than others due to acceptance of some of the system parameters as interval ones. The synthesis method is based on a system poles allocation approach and allows providing the necessary transient process quality in a considered system

РОЗКРИТТЯ ІНФОРМАЦІЇ ПРО НАСЛІДКИ НАДЗВИЧАЙНИХ СИТУАЦІЙ У СИСТЕМІ БУХГАЛТЕРСЬКОГО ОБЛІКУ

Nowadays accounting statements is one of the most dynamic accounting method elements. First and foremost it is related to the correspondence of its subject-matter to the demands of different users willing to know economic conditions in reality changing rapidly. Thus, applying methods of economic analysis on the basis of accounting data it is possible to calculate a range of figures giving an opportunity to estimate both financial condition and economic potential of the enterprise in the future and the past. That is why to calculate such figures in the copes of accounting there should be information about emergency consequences cases affecting the production processes, product cost and further the enterprise’s financial results. This condition will allow estimate their influence on the financial figures and economic potential of the enterprise. The directions of financial statement’s expanding in content and form are articulated. Financial statement is improved in order to reflect information about emergency consequences through expanding factors in already existing chapters (as a part of other costs) and formation of the new chapter V «External and internal risks environmental impact» containing information about separation of emergency consequences from activity costs. Fragments of notes to the annual financial statement are developed giving an opportunity to estimate the impact of emergency consequences on noncurrent and current assets and the production process. Building specific information for internal use about emergency consequences is performed on the basis of justified directions of internal reporting formation and development of ways and mechanisms of their factors formation. It allowed to increase quality of information space of business activity management in emergency conditions. The use of suggestions in practice contributed to increasing the information space quality in users’ decision-making and developing a complex of measures to prevent and address the emergency consequences. In its turn analytical measures calculated on the basis of their facts will take into account a number of factors allowing to fully estimate the financial condition and economic potential.На сьогодні бухгалтерська звітність є одним з найбільш динамічних елементів методу обліку. Перш за все, це пов’язано з відповідністю його предметa вимогам різних користувачів, які бажають дізнатися, що економічні умови в реальності швидко змінюються. Тому, застосовуючи методи економічного аналізу на основі даних бухгалтерського обліку, можна розрахувати діапазон цифр, що дають можливість оцінити як фінансовий стан, так і економічний потенціал підприємства в майбутньому і минулому. Тому для обчислення таких цифр у справах бухгалтерського обліку повинна бути інформація про надзвичайні наслідки, що впливають на виробничі процеси, вартість продукції і фінансові результати підприємства. Ця умова дозволить оцінити їхній вплив на фінансові показники та економічний потенціал підприємства. Сформульовано напрями розширення фінансової звітності за змістом і формою. Фінансова звітність удосконалюється з метою відображення інформації про надзвичайні наслідки за рахунок розширення факторів у наявних главах (як частина інших витрат) і формування нової глави V «Зовнішні та внутрішні ризики впливу на навколишнє середовище», що містить інформацію про відокремлення надзвичайних наслідків від витрати на діяльність. Фрагменти приміток до річної фінансової звітності розроблено, що дає можливість оцінити вплив надзвичайних наслідків на необоротні та оборотні активи і виробничий процес. Побудова конкретної інформації для внутрішнього використання про надзвичайні наслідки здійснюється на основі обґрунтованих напрямів формування внутрішньої звітності та розроблення шляхів і механізмів формування їхніх факторів. Це дозволило підвищити якість інформаційного простору управління діловою діяльністю в надзвичайних умовах. Використання пропозицій на практиці сприяло підвищенню якості інформаційного простору при ухваленні рішень користувачами і розробленні комплексу заходів щодо запобігання надзвичайним наслідкам та їх ліквідації . У свою чергу, аналітичні заходи, розраховані на основі їхніх фактів, ураховуватимуть низку факторів, що дозволяють повністю оцінити фінансовий стан та економічний потенціал

Mechanisms of biotin transport

Biotin is an important micronutrient widely employed as an enzyme cofactor in all living organisms, therefore, cells that cannot synthesize biotin de novo must import it from the external environment. However, most cells have evolved a specific transport protein to facilitate biotin entry into cells, even if they have the necessary biosynthetic pathways, as it is more energetically efficient to scavenge biotin from the environment. The best-characterized examples of biotin transporters now belong to the bacterial energy coupling factor (ECF) family of vitamin transporters that employ similar but distinct mechanisms of solute uptake to the well studied ABC transporters. Here we review recent studies that shed new light on the structure and function of these important proteins. Studies on biotin transporters from organisms outside the bacterial kingdom are also presented, such as the analogous proteins from yeast, mammals and plants. However, there is a paucity of new information here compared to the ECF examples. Possible applications for exploiting biotin transporters for drug delivery are also examined.Al Azhar, Grant W. Booker, and Steven W. Polya

Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality constraints. A number of optimization problems in applications can be stated in this form, examples being the entropy-linear programming, the ridge regression, the elastic net, the regularized optimal transport, etc. We extend the Fast Gradient Method applied to the dual problem in order to make it primal-dual so that it allows not only to solve the dual problem, but also to construct nearly optimal and nearly feasible solution of the primal problem. We also prove a theorem about the convergence rate for the proposed algorithm in terms of the objective function and the linear constraints infeasibility.Comment: Submitted for DOOR 201