The projective method for solving linear matrix inequalities

Numerous problems in control and systems theory can be formulated in terms of linear matrix inequalities (LMI). Since solving an LMI amounts to a convex optimization problem, such formulations are known to be numerically tractable. However, the interest in LMI-based design techniques has really surged with the introduction of efficient interior-point methods for solving LMIs with a polynomial-time complexity. This paper describes one particular method called the Projective Method. Simple geometrical arguments are used to clarify the strategy and convergence mechanism of the Projective algorithm. A complexity analysis is provided, and applications to two generic LMI problems (feasibility and linear objective minimization) are discussed.     

PARTIAL VERSUS GENERAL STORAGE POLICY: COMMODITIES AND RESOURCES

This paper examines joint storage considerations when both commodities and resources can be stored, e.g., grain and water for irrigation. Results suggest that when separate agencies control public resource and commodity storage, suboptimal storage rules occur unless (i) each agency is sensitive to the policies of the other, (ii) commodity inventories are adjusted in response to prices, and (iii) resource inventories are adjusted in response to both commodity demand and resource supply conditions. For example, the common case where water storage depends on weather and reservoir conditions alone is not sufficiently general. The results imply that water management agencies that tend to be dominated by engineers and hydrological considerations need to incorporate economic considerations into decision processes.     

QCM/HCC as a platform for detecting the binding of warfarin to an immobilized film of human serum albumin

Quartz crystal microbalance/heat conduction calorimetry (QCM/HCC) is a new measurement technology that has been used to monitor simultaneously the mass and motional resistance of a thin film in conjunction with the heat flow produced by a chemical change in the film initiated by reaction with a gas. In this work we examine the applicability of the QCM/HCC in detecting chemical changes at the solution/thin film interface. Human serum albumin (HSA) was bound to the gold electrode of a 5 MHz AT-cut quartz resonator using three types of linkers and then exposed to buffered solutions of the anticoagulant drug warfarin. Changes in resonator frequency and motional resistance as well as changes in heat flow produced by warfarin binding to HSA were monitored as a function of the warfarin concentration. Differences in frequency and motional resistance changes depend upon the linker and vary both in magnitude and sign, whereas the integrated heat signal is proportional to the concentration of warfarin and independent of the linker chemistry. Quartz crystal microbalance/heat conduction calorimetry can thus be a useful tool for studying protein-ligand interactions at the solution-surface interface, even though the quartz resonator does not behave as a microbalance.     

On safe tractable approximations of chance constraints

A natural way to handle optimization problem with data affected by stochastic uncertainty is to pass to a chance constrained version of the problem, where candidate solutions should satisfy the randomly perturbed constraints with probability at least 1 − ?. While being attractive from modeling viewpoint, chance constrained problems “as they are” are, in general, computationally intractable. In this survey paper, we overview several simulation-based and simulation-free computationally tractable approximations of chance constrained convex programs, primarily, those of chance constrained linear, conic quadratic and semidefinite programming.     

Metal-stabilized phenoxonium cation

An unprecedented metal-stabilized phenoxonium cation was prepared by a process involving dearomatization of a phenoxy complex. The unique eta2 C=O-metal (iridium) coordination mode leaves the positive charge delocalized within the former aromatic ring. The X-ray structure and conversion into eta2 C=O-coordinated metal-quinone complex are described.     

Self-Concordant Barriers for Convex Approximations of Structured Convex Sets

We show how to approximate the feasible region of structured convex optimization problems by a family of convex sets with explicitly given and efficient (if the accuracy of the approximation is moderate) self-concordant barriers. This approach extends the reach of the modern theory of interior-point methods, and lays the foundation for new ways to treat structured convex optimization problems with a very large number of constraints. Moreover, our approach provides a strong connection from the theory of self-concordant barriers to the combinatorial optimization literature on solving packing and covering problems.