A Full Nesterov-Todd Step Infeasible Interior-point Method for Symmetric Optimization in the Wider Neighborhood of the Central Path

In this paper, an improved Interior-Point Method (IPM) for solving symmetric optimization problems is presented. Symmetric optimization (SO) problems are linear optimization problems over symmetric cones. In particular, the method can be efficiently applied to an important instance of SO, a Controlled Tabular Adjustment (CTA) problem which is a method used for Statistical Disclosure Limitation (SDL) of tabular data. The presented method is a full Nesterov-Todd step infeasible IPM for SO. The algorithm converges to ε-approximate solution from any starting point whether feasible or infeasible. Each iteration consists of the feasibility step and several centering steps, however, the iterates are obtained in the wider neighborhood of the central path in comparison to the similar algorithms of this type which is the main improvement of the method. However, the currently best known iteration bound known for infeasible short-step methods is still achieved.

A New Predictor-corrector Infeasible Interior-point Algorithm for Linear Optimization in aWide Neighborhood

In this paper, we propose a Mizuno-Todd-Ye type predictor-corrector infeasible interior-point method for linear optimization based on a wide neighborhood of the central path. According to Ai-Zhang’s original idea, we use two directions of distinct and orthogonal corresponding to the negative and positive parts of the right side vector of the centering equation of the central path. In the predictor stage, the step size along the corresponded infeasible directions to the negative part is chosen. In the corrector stage by modifying the positive directions system a full-Newton step is removed. We show that, in addition to the predictor step, our method reduces the duality gap in the corrector step and this can be a prominent feature of our method. We prove that the iteration complexity of the new algorithm is 𝒪(n log ɛ−1), which coincides with the best known complexity result for infeasible interior-point methods, where ɛ > 0 is the required precision. Due to the positive direction new system, we improve the theoretical complexity bound for this kind of infeasible interior-point method [1] by a factor of n . Numerical results are also provided to demonstrate the performance of the proposed algorithm.

Features of Dramatic History and Neo-Classicist Elements in Ben Jonson’s Fragment Mortimer His Fall

В статье рассматривается дифференциация и эволюция драматических жанров в конце XVI —начале XVII века в репертуаре английских театров. Отправной точкой нашего исследования служит фрагмент в посмертном собрании Бена Джонсона (1572–1637) наброска «Падение Мортимера», о котором издатель сообщает как о пьесе, не завершенной автором и относящейся к последним месяцам его жизни. Жанр елизаветинской трагедии характеризуется нами как относительно стабильный в течение целого десятилетия. Исходя из наличия у большинства этих пьес содержательных, структурных и художественных особенностей, проверяется принадлежность сцен о Мортимере и Эдуарде III к данной традиции. Анализ фабулы и способов раскрытия основного конфликта в контексте творчества Джонсона и в его отношении к современному театру, прежде всего к шекспировским пьесам, показывает, что незаконченная пьеса «Падение Мортимера» могла быть задумана в период относительного затишья в театральной жизни в середине 1610-х годов. В ней настойчиво реализуются принципы неоклассицизма и отхода от смешения стилевых регистров, которые были характерны для исторических хроник. Ограниченный диапазон действующих лиц, присутствие хоров и групповой диалог, отход от психологической трактовки героя и других персонажей — всё это позволяет заключить, что целью Б. Джонсона было возрождение трагического с национальным содержанием в формах, предписанных античностью. Abstract. The object of analysis is the short-lived, yet unique genre of English dramatic history at the turn of the 16th–187th cc. Emerging in the early years of Elizabeth I’s reign, the history served as a secular replacement of medieval mysteries. The chief features linking histories with the familiar genre of the pre-Reformation tradition were as follows: (1) presence of stock characters; (2) transparent message to the broader audience (religious or national); (3) alternation of low and lofty scenes to provide variety and spectacular turns. At the top of its development, in the 1590s, the history obtained stability of content and diction in the series of William Shakespeare’s tetralogies, to which King John and All’s Trues served as a prologue and epilogue. It would be wrong to exclude Ben Jonson, in so many ways linked to Shakespeare’s work and fame, from participation in the genre practice. Even though he did not contribute dramatized chronicles of Britain’s past for the stage, he tried his hand in Roman tragedies and each conformed to at least two of the features above. In close reading of the surviving part of Ben Jonson’s Mortimer His Fall we distinguish an echo of Elizabethan central path in history, yet evidence of increased Classicist tendencies is much stronger, which suggests new grounds for dating this dramatic sketch.

A primal-dual interior-point method based on a new kernel function for linear complementarity problem

In this paper, we present an interior-point algorithm for solving an optimization problem using the central path method. By an equivalent reformulation of the central path, we obtain a new search direction which targets at a small neighborhood of the central path. For a full-Newton step interior-point algorithm based on this search direction, the complexity bound of the algorithm is the best known for linear complementarity problem. For its numerical tests, some strategies are used and indicate that the algorithm is efficient.

An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an "-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound O ( p rL) using Nesterov-Todd search direction and O (rL) by the xs and sx search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior- point algorithm for this class of mathematical problems.