Algorithms for the continuous nonlinear resource allocation problem---new implementations and numerical studies

Patriksson (2008) provided a then up-to-date survey on the continuous,separable, differentiable and convex resource allocation problem with a single resource constraint. Since the publication of that paper the interest in the problem has grown: several new applications have arisen where the problem at hand constitutes a subproblem, and several new algorithms have been developed for its efficient solution. This paper therefore serves three purposes. First, it provides an up-to-date extension of the survey of the literature of the field, complementing the survey in Patriksson (2008) with more then 20 books and articles. Second, it contributes improvements of some of these algorithms, in particular with an improvement of the pegging (that is, variable fixing) process in the relaxation algorithm, and an improved means to evaluate subsolutions. Third, it numerically evaluates several relaxation (primal) and breakpoint (dual) algorithms, incorporating a variety of pegging strategies, as well as a quasi-Newton method. Our conclusion is that our modification of the relaxation algorithm performs the best. At least for problem sizes up to 30 million variables the practical time complexity for the breakpoint and relaxation algorithms is linear

Fiduciary Duties and Equity-Debtholder Conflicts

We use an important legal event as a natural experiment to examine the effect of management fiduciary duties on equity-debt conflicts. A 1991 Delaware bankruptcy ruling changed the nature of corporate directors' fiduciary duties in firms incorporated in that state. This change limited managers' incentives to take actions favoring equity over debt for firms in the vicinity of financial distress. We show that this ruling increased the likelihood of equity issues, increased investment, and reduced firm risk, consistent with a decrease in debt-equity conflicts of interest. The changes are isolated to firms relatively closer to default. The ruling was also followed by an increase in average leverage and a reduction in covenant use. Finally, we estimate the welfare implications of this change and find that firm values increased when the rules were introduced. We conclude that managerial fiduciary duties affect equity-bond holder conflicts in a way that is economically important, has impact on ex ante capital structure choices, and affects welfare.

Ditching Your Duty: When Must Private Entities Comply with Federal Antidiscrimination Law?

This Commentary considers how the Fifth Circuit characterizes “services, programs, and activities” of public agencies in Ivy v. Williams, in the context of determining whether a private entity is subject to federal antidiscrimination law. “Services, programs, and activities” of public agencies must comply with Title II of the Americans with Disabilities Act, whether directly distributed by a public or a private entity. This Commentary argues private driving schools in Texas that distribute a driving course necessary to obtaining a drivers’ license are subject to Title II because the providing the course functionally constitutes a program of the Texas Education Agency, a public agency. Though this case was dismissed as moot by the Supreme Court on technical grounds, the issue remains poignant

Leveraged Buyouts and Private Equity

We describe and present time series evidence on the leveraged buyout/private equity industry, both firms and transactions. We discuss the existing empirical evidence on the economics of the firms and transactions. We consider similarities and differences between the recent private equity wave and the wave of the 1980s. Finally, we speculate on what the evidence implies for the future of private equity.PrivateEquity

Private Equity and Long-Run Investment: The Case of Innovation

A long-standing controversy is whether LBOs relieve managers from short-term pressures from public shareholders, or whether LBO funds themselves are driven by short-term profit motives and sacrifice long-term growth to boost short-term performance. We investigate 495 transactions with a focus on one form of long-term activities, namely investments in innovation as measured by patenting activity. We find no evidence that LBOs are associated with a decrease in these activities. Relying on standard measures of patent quality, we find that patents granted to firms involved in private equity trans actions are more cited (a proxy for economic importance), show no significant shifts in the fundamental nature of the research, and are more concentrated in the most important and prominent areas of companies' innovative portfolios.Private equity; patents; innovation; short-termism