Using a Factored Dual in Augmented Lagrangian Methods for Semidefinite Programming

In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on how to deal with the resulting unconstrained maximization of the augmented Lagrangian are given. We further use the approximate maximum of the augmented Lagrangian with the aim of improving the convergence rate of alternating direction augmented Lagrangian frameworks. Numerical results are reported, showing the benefits of the approach.Comment: 7 page

Using a conic bundle method to accelerate both phases of a quadratic convex reformulation

We present algorithm MIQCR-CB that is an advancement of method MIQCR~(Billionnet, Elloumi and Lambert, 2012). MIQCR is a method for solving mixed-integer quadratic programs and works in two phases: the first phase determines an equivalent quadratic formulation with a convex objective function by solving a semidefinite problem $(SDP)$, and, in the second phase, the equivalent formulation is solved by a standard solver. As the reformulation relies on the solution of a large-scale semidefinite program, it is not tractable by existing semidefinite solvers, already for medium sized problems. To surmount this difficulty, we present in MIQCR-CB a subgradient algorithm within a Lagrangian duality framework for solving $(SDP)$ that substantially speeds up the first phase. Moreover, this algorithm leads to a reformulated problem of smaller size than the one obtained by the original MIQCR method which results in a shorter time for solving the second phase. We present extensive computational results to show the efficiency of our algorithm

Exact Algorithms for the Quadratic Linear Ordering Problem

The quadratic linear ordering problem naturally generalizes various optimization problems, such as bipartite crossing minimization or the betweenness problem, which includes linear arrangement. These problems have important applications in, e.g., automatic graph drawing and computational biology. We present a new polyhedral approach to the quadratic linear ordering problem that is based on a linearization of the quadratic objective function. Our main result is a reformulation of the 3-dicycle inequalities using quadratic terms, the resulting constraints are shown to be face-inducing for the polytope corresponding to the unconstrained quadratic problem. We exploit this result both within a branch-and-cut algorithm and within an SDP-based branch-and-bound algorithm. Experimental results for bipartite crossing minimization show that this approach clearly outperforms other methods

ON THE COMPLEXITY OF SEMIDEFINITE PROGRAMS ARISING IN POLYNOMIAL OPTIMIZATION

In this paper we investigate matrix inequalities which hold irrespective of the size of the matrices involved, and explain how the search for such inequalities can be implemented as a semidefinite program (SDP). We provide a comprehensive discussion of the time complexity of these SDPs

Exact Algorithms for the Quadratic Linear Ordering Problem

The quadratic linear ordering problem naturally generalizes various optimization problems, such as bipartite crossing minimization or the betweenness problem, which includes linear arrangement. These problems have important applications in, e.g., automatic graph drawing and computational biology. We present a new polyhedral approach to the quadratic linear ordering problem that is based on a linearization of the quadratic objective function. Our main result is a reformulation of the 3-dicycle inequalities using quadratic terms, the resulting constraints are shown to be face-inducing for the polytope corresponding to the unconstrained quadratic problem. We exploit this result both within a branch-and-cut algorithm and within an SDP-based branch-and-bound algorithm. Experimental results for bipartite crossing minimization show that this approach clearly outperforms other methods

Surprising Comparison Of Risk And Return Factors Between Real Estate Investment Trusts (REITs) And The S&P 500 Index During The 2000-2011 Time Period

We composed and contrasted stock returns for large capitalized companies (S&P 500) with returns of real estate investment trusts using the Financial Times equity, mortgage and composite indexes. The time period which was chosen was 2000 through 2011. This period is significant because up until the crash of 2008, the real estate bubble was forming. Major real estate problems were already in force in 2007, but serious deflation really did not fully commence until the stock market crash in the late summer and early fall of 2008. With such heavy doses of deflation, one would think real estate was doomed. We found that average returns for the S&P 500 during this time period was 2.44% vs. a 13.73% average return for the composite Real Estate Investment Trusts (REIT) index. We calculated the geometric returns of .0054% for the S&P 500 vs. 11.21% for the composite REIT. This geometric return calculation was necessary because of many negative returns over a short period of time. The real surprise came when we risk adjusted our numbers using coefficients of variation. Using average returns, we found that the S&P 500 took 7.9959 units of risk for each unit of return, while the composite REIT composite only took 1.6497 units of risk per return. Even the SE Mortgage index only took 2.4914 units of risk per unit of return, while the Equity REIT index took on 1.5744 units of risk per return. Utilizing geometric returns or compounded rates of return, we found a coefficient of variation (CV) of 9.755 for the S&P 500, where the composite REIT experienced a 2.0205 CV and the FTSE Mortgage index showed a 4.0023 CV. Even though mortgage REITs took a greater hit than equity REITs, we still found a favorable relationship of risk and return vs. investment in common stocks. Money managers, who were properly diversified, rode out the financial storm much more comfortably with REITs as part of their diversification parameters

Die Inszenierung von Geschlecht, Sexualität und Macht in Federico García Lorcas "La casa de Bernarda Alba"

In meiner Arbeit analysiere ich die männlichen und weiblichen Geschlechterrollen in "La casa de Bernarda Alba", sowie die Inszenierung von Sexualität als Tabu und unbezwingbaren Trieb. Anhand von Lorcas Drama "La casa de Bernarda Alba" zeige ich welche gender Diskurse im 19. und 20. Jahrhundert in Spanien vorherrschten. Die Geschlchternormen setze ich in Bezug zur realen Lebenssituation von Männern und Frauen im ländlichen Andalusien. Dabei konzentriere ich mich auf die Arbeitsbedingungen, die Bildungsvoraussetzungen für Frauen, sowie die rechtlichen Aspekte, die das Zusammenleben von Mann und Frau regelten. Lorcas Stück ist ein eminentes Beispiel für die Macht der Gender Diskurse und die Kritik an einem traditionellen, katholischen, patriarchalen und autoritären System, das Anfang des 20. Jahrhunderts die spanische Gesellschaft noch zu einem großen Teil bestimmte.In my diploma thesis I have analyzed the power of gender codes over the spanish reality in the 19th and 20th century. The gender norms influenced the lives of women and men in rural Andalusia in a very deep way: controlling their behaviour, regulating their sexuality (especially female sexuality) and dictating e. g. their work options. Based on García Lorcas tragic play "The house of Bernarda Alba" I tried to exemplify the reality of gender discourse and its impact on art and theatre. The author himself, as a homosexual, knew the power of the heterosexual matrix, as described by Judith Butler, and in his play he undermines the traditional, catholic values of honor which had still a great impact on spanish society at the beginning of the 20th century