Convex Cost Research Articles

Total activation: fMRI deconvolution through spatio-temporal regularization

Confirmatory approaches to fMRI data analysis look for evidence for the presence of pre-defined regressors modeling contributions to the voxel time series, including the BOLD response following neuronal activation. As more complicated questions arise about brain function, such as spontaneous and resting-state activity, new methodologies are required. We propose total activation (TA) as a novel fMRI data analysis method to explore the underlying activity-inducing signal of the BOLD signal without any timing information that is based on sparse spatio-temporal priors and characterization of the hemodynamic system. Within a variational framework, we formulate a convex cost function-including spatial and temporal regularization terms-that is solved by fast iterative shrinkage algorithms. The temporal regularization expresses that the activity-inducing signal is block-type without restrictions on the timing nor duration. The spatial regularization favors coherent activation patterns in anatomically-defined brain regions. TA is evaluated using a software phantom and an event-related fMRI experiment with prolonged resting state periods disturbed by visual stimuli. The results illustrate that both block-type and spike-type activities can be recovered successfully without prior knowledge of the experimental paradigm. Further processing using hierarchical clustering shows that the activity-inducing signals revealed by TA contain information about meaningful task-related and resting-state networks, demonstrating good abilities for the study of non-stationary dynamics of brain activity.

Discussion on “A GA-API Solution for the Economic Dispatch of Generation in Power System Operation”

The commentors feel the authors of the above-named article [ibid., vol. 27, no. 1, pp. 233-242, Feb. 2012] that presents a hybrid heuristic method combining real coded genetic algorithm and special class of ant colony optimization for economic dispatch (ED) problems is commendable. The feasibility of the proposed method to solve ED is shown, by experimenting with four test systems considering 3, 6, 15, and 40 units with convex and nonconvex cost functions and also three benchmark functions. However, we would like to seek the authors' clarification regarding four particular points.

Discussion on “A GA-API Solution for the Economic Dispatch of Generation in Power System Operation”

The authors' effort in presenting a hybrid heuristic method combining real coded genetic algorithm and special class of ant colony optimization for economic dispatch (ED) problems is commendable. The feasibility of the proposed method to solve ED is shown, by experimenting with four test systems considering 3, 6, 15, and 40 units with convex and nonconvex cost functions and also three benchmark functions.

Production planning under uncertainty: the case of hydrothermal systems

This paper formulates the hydrothermal production planning problem as a multi-stage stochastic programming model. This problem is usually solved using algorithms that are based on dynamic programming and nested Benders decomposition (NBD). The hydrothermal planning problem is remodelled as a capacitated production planning model with convex costs; then a vanishing effect property of the first period decision is derived. Based on this property, a special implementation scheme of the NBD algorithm is proposed, providing faster convergence and less computational effort. The NBD algorithm is implemented for a large-scale hydrothermal power system of the Pacific Northwest in the USA with 20 thermal plants and 21 thermal plants.

Balanced Min Cost Flow on Skew Symmetric Networks with Convex Costs

We consider the solution of matching problems with a convex cost function via a network flow algorithm. We review the general mapping between matching problems and flow problems on skew symmetric networks and revisit several results on optimality of network flows. We use these results to derive a balanced capacity scaling algorithm for matching problems with a linear cost function. The latter is later generalized to a balanced capacity scaling algorithm also for a convex cost function. We prove the correctness and discuss the complexity of our solution.

Network Security and Contagion

We develop a theoretical model of security investments in a network of interconnected agents. Network connections introduce the possibility of cascading failures, due to an exogenous or endogenous attack, depending on the profile of security investments by the agents. The general presumption in the literature, based on intuitive arguments or analysis of symmetric networks, is that because security investments create positive externalities on other agents, there will be under-investment in security. We show that this reasoning is incomplete because of a first-order economic force: security investments are also strategic substitutes. In a general (non-symmetric) network, this implies that under-investment by some agents will encourage over-investment by others. We demonstrate, by means of examples, there can be over-investment by some agents, and also that aggregate probabilities of infection can be lower in equilibrium compared to the social optimum. We then provide sufficient conditions for under-investment. This requires both sufficiently convex cost functions, (convexity alone is not enough), and networks that are either symmetric or locally tree-like. We also characterize the impact of network structure on equilibrium and optimal investments. Finally, we show that when the attack location is endogenized, (by assuming that the attacker chooses a probability distribution over the location of the attack in order to maximize damage), there is an additional incentive for over-investment: greater investment by an agent shifts the attack to other parts of the network.

The Inventory Growth Spread

Previous studies show that firms with low inventory growth outperform firms with high inventory growth in the cross-section of publicly traded firms. In addition, inventory investment is volatile and procyclical, and inventory-to-sales is persistent and countercyclical. We embed an inventory holding motive into the investment-based asset pricing framework by modeling inventory as a factor of production with convex and nonconvex adjustment costs. The augmented model simultaneously matches the large inventory growth spread in the data, as well as the time-series properties of the firm level capital investment, inventory investment, and inventory-to-sales. Our conditional single-factor model also implies that traditional unconditional factor models such as the CAPM should fail to explain the inventory growth spread, although not with the same large pricing errors observed in the data.

Binary Compressed Imaging

Compressed sensing can substantially reduce the number of samples required for conventional signal acquisition at the expense of an additional reconstruction procedure. It also provides robust reconstruction when using quantized measurements, including in the one-bit setting. In this paper, our goal is to design a framework for binary compressed sensing that is adapted to images. Accordingly, we propose an acquisition and reconstruction approach that complies with the high dimensionality of image data and that provides reconstructions of satisfactory visual quality. Our forward model describes data acquisition and follows physical principles. It entails a series of random convolutions performed optically followed by sampling and binary thresholding. The binary samples that are obtained can be either measured or ignored according to predefined functions. Based on these measurements, we then express our reconstruction problem as the minimization of a compound convex cost that enforces the consistency of the solution with the available binary data under total-variation regularization. Finally, we derive an efficient reconstruction algorithm relying on convex-optimization principles. We conduct several experiments on standard images and demonstrate the practical interest of our approach.

One-Dimensional Numerical Algorithms for Gradient Flows in the p-Wasserstein Spaces

We numerically approximate, on the real line, solutions to a large class of parabolic partial differential equations which are "gradient flows" of some energy functionals with respect to the L p -Wasserstein metrics for all p>1. Our method relies on variational principles involving the optimal transport problem with general strictly convex cost functions.

Asynchronous Newton-Raphson Consensus for Distributed Convex Optimization

We consider the distributed unconstrained minimization of separable convex cost functions, where the global cost is given by the sum of several local and private costs, each associated to a specific agent of a given communication network. We specifically address an asynchronous distributed optimization technique called Newton-Raphson Consensus. Beside having low computational complexity, low communication requirements and being interpretable as a distributed Newton-Raphson algorithm, the technique has also the beneficial properties of requiring very little coordination and naturally supporting time-varying topologies. In this work we analytically prove that under some assumptions it shows either local or global convergence properties, and corroborate this result by the means of numerical simulations.

Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics

In this paper we present a spatially-adaptive method for image reconstruction that is based on the concept of statistical multiresolution estimation as introduced in Frick et al. (Electron. J. Stat. 6:231---268, 2012). It constitutes a variational regularization technique that uses an ? ?-type distance measure as data-fidelity combined with a convex cost functional. The resulting convex optimization problem is approached by a combination of an inexact alternating direction method of multipliers and Dykstra's projection algorithm. We describe a novel method for balancing data-fit and regularity that is fully automatic and allows for a sound statistical interpretation. The performance of our estimation approach is studied for various problems in imaging. Among others, this includes deconvolution problems that arise in Poisson nanoscale fluorescence microscopy.

Collusion in experimental Bertrand duopolies with convex costs: The role of cost asymmetry

Theory, experimental studies, as well as antitrust guidelines suggest that symmetry among firms is conducive to more collusive outcomes. We test this perception in a series of experimental repeated Bertrand duopolies where firms have convex costs. We implement symmetric as well as asymmetric markets that vary in their degree of cost asymmetry among firms. We find no evidence of symmetric markets being more prone to collusion than asymmetric markets. If anything, asymmetry helps firms coordinate on higher prices and achieve higher profits.

The single-server scheduling problem with convex costs

Being probably one of the oldest decision problems in queuing theory, the single-server scheduling problem continues to be a challenging one. The original formulations considered linear costs, and the resulting policy is puzzling in many ways. The main one is that, either for preemptive or nonpreemptive problems, it results in a priority ordering of the different classes of customers being served that is insensitive to the individual load each class imposes on the server and insensitive to the overall load the server experiences. This policy is known as the cμ-rule. We claim and show that for convex costs, the optimal policy depends on the individual loads. Therefore, there is a need for an alternative generalization of the cμ-rule. The main feature of our generalization consists on first-order differences of the single stage cost function, rather than on its derivatives. The resulting policy is able to reach near optimal performances and is a function of the individual loads.

Discussion of “Bhattacharya, A., & Chattopadhyay, P. K. (2010). Solving complex economic load dispatch problems using biogeography-based optimization. Expert Systems with Applications, 37(5), 3605–3615”

This Paper presents a discussion of “Solving complex economic load dispatch problems using biogeography-based optimization” by Aniruddha Bhattacharya et al. (2010). Expert Systems with Applications (37) (pp. 3605–3615). The discussed paper presented economic load dispatch problem by experimenting with four example systems considering convex and nonconvex cost functions. Biogeography-based optimization (BBO) applied to 10-generator system with valve-point effects and multiple fuels. However in the reported results for the 10-generator system total fuel cost calculation is different for the given generation schedule. In this communication, clarification regarding cost calculation was presented.

On the uniqueness of Cournot equilibrium in case of concave integrated price flexibility

We consider a class of homogeneous Cournot oligopolies with concave integrated price flexibility and convex cost functions. We provide new results about the semi-uniqueness and uniqueness of (Cournot) equilibria for the oligopolies that satisfy these conditions. The condition of concave integrated price flexibility is implied by (but does not imply) the log-concavity of a continuous decreasing price function. So, our results generalize previous results for decreasing log-concave price functions and convex cost functions. We also discuss the particular type of quasi-concavity that characterizes the conditional revenue and profit functions of the firms in these oligopolies and we point out an error of the literature on the equilibrium uniqueness in oligopolies with log-concave price functions. Finally, we explain how the condition of concave integrated price flexibility relates to other conditions on the price and aggregate revenue functions usually considered in the literature, e.g., their concavity.

Overdissipation and Convergence in Rent-Seeking Experiments: Cost Structure and Prize Allocation Rules

We study experimentally the effects of cost structure and prize allocation rules on the performance of rent-seeking contests. Most previous studies use a lottery prize rule and linear cost, and find both overdissipation relative to Nash equilibrium prediction and significant variation in individual subject efforts. In a 2 x 2 design, we investigate the effects of sharing the prize proportionally and of a convex cost function, while holding fixed the Nash equilibrium prediction for effort. We find that the share rule results in average effort closer to the Nash prediction, lower variation in individual efforts, and convergence of the distribution of individual efforts towards Nash over time. Combining the share rule with a convex cost function further enhances these results. Our findings indicate that a significant amount of subjects’ non-equilibrium behavior in contests can be explained by features of the experimental design. These results contribute towards design guidelines for contests based on behavioral principles that take into account contest features that may not affect the Nash equilibrium prediction. These lessons suggest design guidelines for future experiments on contests.

Projeto de rede com custos convexos e balanceamento de fluxos

O problema de projeto de redes arborescentes de fonte única com custos convexos é abordado neste trabalho. Trata-se de problema referencial no projeto de redes de transporte de matéria, energia ou informação. Resulta do esforço de modelagem um programa não-linear inteiro misto de grande escala e de difícil resolução. Para superar tais dificuldades, dois métodos distintos são aplicados ao problema: O primeiro deles é a técnica de Decomposição de Benders Generalizada; o segundo método combina a técnica de Aproximação Externa com as idéias de projeção subjacentes à Decomposição de Benders para derivar a técnica OA-Híbrido. O método OA-Híbrido se mostra muito eficiente na solução de instâncias com até 702 arcos, obtendo custos de computação bastante razoáveis, tornando promissora a sua aplicação a problemas ainda mais sofisticados.

Strict Concavity of the Value Function for a Family of Dynamic Accumulation Models

We prove strict concavity of the value function for liquidity constrained dynamic accumulation models without adopting at least one of the following restrictive assumptions: zero response of productive effort, bounded marginal value of accumulated balances, or strictly convex cost of holding accumulated balances. Thus we extend well known theoretical results to more general models of saving with liquidity constraints and of commodity storage with non-negativity constraints on stocks. Our results provide a foundation for estimation of a homogeneous markovian process for consumption in models of saving, or for price in commodity storage models, under more realistic assumptions.

Timing and Self-Control

The dual self-model of self-control with one-period lived short-run selves is excessively sensitive to the timing of shocks and to the interpolation of additional no- action time periods in between the dates when decisions are made. We show that when short-run selves have a random length of time this excess sensitivity goes away. We consider both linear and convex cost of self-control models, illustrating the theory through a series of examples. We examine when opportunities to consume will be avoided or delayed; we consider the way in which the marginal interest declines with delay, and we examine how preference reversals depend on the timing of information. To accommodate the combination of short time periods and convex costs of self control we extend the model to treat willpower as a cognitive resource that is limited in the short run.

Lower Semicontinuity of the Solution Set to a Parametric Optimal Control Problem

This paper studies the solution stability of a parametric optimal control problem with linear state equation, control constraints, and convex cost functions. By reducing the problem to a parametric programming problem and a parametric variational inequality, we obtain the lower semicontinuity of the solution map to a parametric optimal control problem.