A new algorithm for generalized fractional programs

A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual†to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual†parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual†approach is less influenced by scaling.fractional programming;generalized fractional programming;Dinkelbach-type algorithms;quasiconvexity;Karush-Kuhn-Tucker conditions;duality

Generalized Nash Equilibrium and Market Coupling in the European Power System

Market Coupling'' is currently seen as the most advanced market design in the restructuring of the European electricity market. Market coupling, by construction, introduces what is generally referred to as an incomplete market: it leaves several constraints out of the market and hence avoids pricing them. This may or may not have important consequences in practice depending on the case on hand. QuasiVariational Inequality problems. We apply one of these methods to a subproblem of market coupling namely the coordination of counter-trading. This problem is an illustration of a more general question encountered for instance in hierarchical planning in production management. We first discuss the economic interpretation of the Quasi-Variational Inequality problem. We then apply the algorithmic approach to a set of stylized case studies in order to illustrate the impact of different organizations of counter-trading. The paper emphazises the structuring of the problem. A companion paper considers the full problem of market coupling and counter-trading and presents a more extensive numerical analysis

A new algorithm for generalized fractional programs

A new dual problem for convex generalized fractional programs with no duality gap is presented and it is shown how this dual problem can be efficiently solved using a parametric approach. The resulting algorithm can be seen as “dual” to the Dinkelbach-type algorithm for generalized fractional programs since it approximates the optimal objective value of the dual (primal) problem from below. Convergence results for this algorithm are derived and an easy condition to achieve superlinear convergence is also established. Moreover, under some additional assumptions the algorithm also recovers at the same time an optimal solution of the primal problem. We also consider a variant of this new algorithm, based on scaling the “dual” parametric function. The numerical results, in case of quadratic-linear ratios and linear constraints, show that the performance of the new algorithm and its scaled version is superior to that of the Dinkelbach-type algorithms. From the computational results it also appears that contrary to the primal approach, the “dual” approach is less influenced by scaling

Light-induced hexatic state in a layered quantum material

The tunability of materials properties by light promises a wealth of future applications in energy conversion and information technology. Strongly correlated materials such as transition-metal dichalcogenides (TMDCs) offer optical control of electronic phases, charge ordering and interlayer correlations by photodoping. Here, we find the emergence of a transient hexatic state in a TMDC thin-film during the laser-induced transformation between two charge-density wave (CDW) phases. Introducing tilt-series ultrafast nanobeam electron diffraction, we reconstruct CDW rocking curves at high momentum resolution. An intermittent suppression of three-dimensional structural correlations promotes a loss of in-plane translational order characteristic of a hexatic intermediate. Our results demonstrate the merit of tomographic ultrafast structural probing in tracing coupled order parameters, heralding universal nanoscale access to laser-induced dimensionality control in functional heterostructures and devices

Duality for equilibrium problems under generalized monotonicity

Duality is studied for an abstract equilibrium problem which includes, among others, optimization problems and variational inequality problems. Following different schemes, various duals are proposed and primal-dual relationships are established under certain generalized convexity and generalized monotonicity assumptions. In a primal-dual setting, existence results for a solution are derived for different generalized monotone equilibrium problems within each duality scheme

Reporting of sex as a variable in cardiovascular studies using cultured cells

<p>Abstract</p> <p>Background</p> <p>Chromosomal complement, including that provided by the sex chromosomes, influences expression of proteins and molecular signaling in every cell. However, less than 50% of the scientific studies published in 2009 using experimental animals reported sex as a biological variable. Because every cell has a sex, we conducted a literature review to determine the extent to which sex is reported as a variable in cardiovascular studies on cultured cells.</p> <p>Methods</p> <p>Articles from 10 cardiovascular journals with high impact factors (<it>Circulation</it>, <it>J Am Coll Cardiol</it>, <it>Eur Heart J</it>, <it>Circ Res</it>, <it>Arterioscler Thromb Vasc Biol</it>, <it>Cardiovasc Res</it>, <it>J Mol Cell Cardiol</it>, <it>Am J Physiol Heart Circ Physiol</it>, <it>J Heart Lung Transplant and J Cardiovasc Pharmacol</it>) and published in 2010 were searched using terms 'cultured' and 'cells' in any order to determine if the sex of those cells was reported. Studies using established cell lines were excluded.</p> <p>Results</p> <p>Using two separate search strategies, we found that only 25 of 90 articles (28%) and 20 of 101 articles (19.8%) reported the sex of cells. Of those reporting the sex of cells, most (68.9%; n = 31) used only male cells and none used exclusively female cells. In studies reporting the sex of cells of cardiovascular origin, 40% used vascular smooth-muscle cells, and 30% used stem/progenitor cells. In studies using cells of human origin, 35% did not report the sex of those cells. None of the studies using neonatal cardiac myocytes reported the sex of those cells.</p> <p>Conclusions</p> <p>The complement of sex chromosomes in cells studied in culture has the potential to affect expression of proteins and 'mechanistic' signaling pathways. Therefore, consistent with scientific excellence, editorial policies should require reporting sex of cells used in <it>in vitro </it>experiments.</p

Combined relaxation method for mixed equilibrium problems

We consider a general class of equilibrium problems which involve a single-valued mapping and a nonsmooth bifunction. Such mixed equilibrium problems are solved with a combined relaxation method using an auxiliary iteration of a splitting-type method for constructing a separating hyperplane. We prove the convergence of the method under the assumption that the dual of the mixed equilibrium problem is solvable. Convergence rates are also derived. © 2005 Springer Science+Business Media, Inc

Gauss-Seidel method for multi-valued inclusions with Z mappings

We consider a problem of solution of a multi-valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss-Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under rather mild additional assumptions. Some results of numerical experiments are also presented. © 2011 Springer Science+Business Media, LLC

Noncooperative games with vector payoffs under relative pseudomonotonicity

We consider the Nash equilibrium problem with vector payoffs in a topological vector space. By employing the recent concept of relative (pseudo) monotonicity, we establish several existence results for vector Nash equilibria and vector equilibria. The results strengthen in a major way existence results for vector equilibrium problems which were based on the usual (generalized) monotonicity concepts

Gauss-Seidel method for multi-valued inclusions with Z mappings

We consider a problem of solution of a multi-valued inclusion on a cone segment. In the case where the underlying mapping possesses Z type properties we suggest an extension of Gauss-Seidel algorithms from nonlinear equations. We prove convergence of a modified double iteration process under rather mild additional assumptions. Some results of numerical experiments are also presented. © 2011 Springer Science+Business Media, LLC