Constrained Maximization Research Articles

Signaling through Bayesian persuasion

This paper examines the conditions under which separating outcomes occur in informed persuasion, that is, in Bayesian persuasion settings in which the sender is privately informed about the payoff-relevant state prior to committing to an experiment. We consider a setting with finite payoff-relevant states and sender payoffs that are continuous and monotonic in the receiver’s posterior beliefs. The paper finds that if full disclosure of the payoff-relevant state reduces the sender’s expected payoff under any common prior (i.e., if the sender’s payoff function is outer concave), then single-crossing properties arise such that the high sender type can separate from the low type by choosing more informative experiments. This single-crossing condition leads to the selection of “least costly” separating equilibria by the D1 criterion, i.e., the sender’s choice of experiment signals his type. Further, separating equilibria are characterized by simple constrained maximization problems.

Financial Hedging of Operational Risk Constraints: A General Framework

We consider the operation of a non-financial corporation and present a novel risk-management framework that supports the joint optimization of the firm’s operational and financial decisions. Specifically, we study the problem of maximizing the firm’s operating profits when these profits depend on movements in the financial markets, and where the decision maker—the firm’s manager—is risk averse. Critically, our framework (i) imposes risk aversion through a generic class of risk constraints, and (ii) considers explicitly the differences that can exist between the shareholders’ and manager’s beliefs about future market risks. Together, these aspects allow us to remove speculation so that financial instruments can only be used for hedging purposes. We analyze our problem in an incomplete financial market setting and consider different informational assumptions. Within this framework, we characterize the optimal financial hedging strategy so that the problem reduces to a constrained maximization over operational policies. Our results show how financial hedging can be effectively used to expand the set of admissible operating policies, and identify conditions under which the risk constraint can be completely ignored when solving for an optimal operating policy. We illustrate our methodology in the context of an exporter firm which faces exchange rate risk in trading.

Constrained Maximization of the Economic Production Model of Lithium Ore Exploration in Nasarawa

Over 20,000 years ago, mining was discovered as one of the oldest production industries generating over US$700 billions’ of revenue in the world by a few mining companies. For some time, mining work has resulted in a very demanding affair as a result of greater depth, low-grade, limited resources, and complex geo-mining conditions. Therefore, optimization of the mining system plays a vital role in profit maximization with the satisfaction of many constraints. However, today’s mining industry uses complex and sophisticated systems whose reliability has become a critical issue. This work adopted the financial market theory of development to propose a maximized constrained optimization economic production model for lithium ore exploration in Nasarawa, Nigeria using three methods such as: the break-even principle method of cut-off grade between revenue earned and cost incurred; the mortimer’s method principle to determine ore based in two cut-off criteria (original and average good) and the lane method for net profit value thereby maximizing processing capacity. Data obtained from the field and the Ministry of Mines and Solid Minerals were analyzed using energy dispersive x-ray fluorescence (EDXRF) showing the presence of lithium. The froth flotation technique used showed the beneficiation thereby achieving improved lithium concentrates and the inductively coupled atomic emission revealed a high presence of lithium of over 1859 parts per million (ppm) and other minerals.

Budget-Constrained Linear Utility Maximization and the Hurwicz (1951) Criterion

We show that for a trader displaying state-dependent risk-neutrality, budget constrained maximization based on the Hurwicz criterion for “non-probabilistic” uncertainty with the degree of pessimism being less than half, reduces to expected utility maximization under “the equal ignorance principle”, with all wealth being invested in positive return being available in just one state of nature and nothing at all in other states of nature. Such a portfolio is an extreme point of the set of budget-constrained expected utility maximizing portfolios, with equiprobable states of nature. With more than two uncertain states of nature, the above result extends to the case where the degree of pessimism is equal to half. We also show that if for a degree of pessimism, greater than or equal to half, an optimal solution to budget constrained maximization based on the Hurwicz criterion is not of this type, then it must be a “budget-constrained max-min utility maximizing” portfolio.

Bringing the Doctor to the Patients: Cardiology Outreach to Rural Areas

Clinical outreach is a crucial but understudied health care service delivery model. Physicians staffing rural outreach clinics must allocate a limited resource (i.e., their time) between caring for patients at their main sites and outreach locations. Using a unique 30-year data set of decisions made by cardiologists, the authors estimate a constrained utility maximization model of time allocations across home and outreach locations. The results show that travel distance, potential competition, and patient demand for cardiology services significantly influence allocation decisions. This structural model is used to simulate the impact of a predicted reduction in cardiologist supply. The expected impacts are unevenly distributed, with some rural locations experiencing large decreases in access. The authors evaluate two policies to restore rural access: targeted immigration and a subsidy program. A subsidy program with an estimated annual cost of $406,000 can restore outreach after a 10% reduction in cardiologist supply. This option should be preferred to recruiting and supporting five additional cardiologists under a targeted immigration strategy. This research demonstrates the value of marketing modeling in addressing limited access to health care services and evaluating alternative policies for maintaining access in the face of coming physician shortages.

Characterization of planetary regolith simulants for the research and development of space resource technologies

Human planetary exploration and colonization efforts are reliant on the ability to safely interact with planetary surfaces and to leverage local regolith as a resource. The high-cost and risk-intensive nature of establishing planetary infrastructure and resource utilization facilities necessitates risk reduction through laboratory-based research and development of space resource acquisition, processing, and extraction technologies using appropriate, well-characterized, mineral-based regolith simulants. Such simulants enable the planetary exploration and resource utilization communities to test large-scale technologies and methodologies for a relatively low cost as an alternative to scarce and expensive returned samples. The fidelity of a regolith simulant for any application is, in part, determined by the mineralogical composition and particle size distribution. The importance of composition is well established for in situ resource utilization studies sensitive to geochemical properties but tends to be ignored in studies concerned with physical properties. Neglecting to consider mineralogy reduces the fidelity of a simulant since each mineral species has its own unique grain density, preferred grain geometry, and intergranular forces, all of which affect the physical properties of the simulant (e.g., shear strength, bearing strength, bulk density, thermal and electrical properties, magnetic properties). Traditionally, regolith simulants have been limited in quantity and availability; Exolith Lab remedies these problems by designing simulants in a constrained maximization approach to fidelity relative to cost, material availability, and safety. Exolith Lab simulants are designed to approximate the mineralogy and particle size ranges of the planetary regolith being simulated, with composition constrained by remote sensing observations and/or returned sample analyses. With facilities and equipment capable of high-volume simulant production, Exolith Lab offers standard simulants in bulk that are readily available for purchase and shipment. This work reviews the production methods, equipment, and materials used to create Exolith Lab simulants, provides compositional data, particle size data, and applications for each standard lunar, Martian, and asteroid simulant that Exolith Lab offers.

Adjusted empirical likelihood for probability density functions under strong mixing samples

To obtain a profile empirical likelihood ratio statistic is essentially to address a constrained maximization problem. However, when sample size is small, the optimal function may have no numerical solution, as the convex hull of the sample points may not contain the zero vector 0 as its interior point. The adjusted empirical likelihood (AEL) method introduced by Chen, Variyath, and Abraham (2008) is very useful to solve this problem. The innovation of this article is that we extend the AEL method to probability density functions (p.d.f.) under dependent samples, as there are few literatures using this method under dependent samples. It is shown that the AEL ratio statistic for a p.d.f. is asymptotically χ 2 -type distributed under a mixing sample, which is used to obtain an AEL-based confidence interval for the p.d.f. Our simulations show that the AEL is faster to compute than unadjusted empirical likelihood and the coverage probability based on the AEL method is superior to the other two usual methods, namely the unadjusted empirical likelihood and the normal approximation methods, particularly under small sample sizes.

CEM: Constrained Entropy Maximization for Task-Agnostic Safe Exploration

In the absence of assigned tasks, a learning agent typically seeks to explore its environment efficiently. However, the pursuit of exploration will bring more safety risks. An under-explored aspect of reinforcement learning is how to achieve safe efficient exploration when the task is unknown. In this paper, we propose a practical Constrained Entropy Maximization (CEM) algorithm to solve task-agnostic safe exploration problems, which naturally require a finite horizon and undiscounted constraints on safety costs. The CEM algorithm aims to learn a policy that maximizes state entropy under the premise of safety. To avoid approximating the state density in complex domains, CEM leverages a k-nearest neighbor entropy estimator to evaluate the efficiency of exploration. In terms of safety, CEM minimizes the safety costs, and adaptively trades off safety and exploration based on the current constraint satisfaction. The empirical analysis shows that CEM enables the acquisition of a safe exploration policy in complex environments, resulting in improved performance in both safety and sample efficiency for target tasks.

Streaming Algorithms for Constrained Submodular Maximization

Due to the pervasive "diminishing returns" property appeared in data-intensive applications, submodular maximization problems have aroused great attention from both the machine learning community and the computation theory community. During the last decades, a lot of algorithms have been proposed for submodular maximization subject to various constraints [4, 6, 8], and these algorithms can be used in numerous applications including sensor placement [9], clustering [5], network design [13], and so on. The existing algorithms for submodular maximization can be roughly classified into offline algorithms and streaming algorithms; the former assume full access to the whole dataset at any time (e.g.,[4, 10]), while the latter only require an amount of space which is nearly linear in the maximum size of a feasible solution (e.g., [1, 7]). Apparently, streaming algorithms are more useful in big data applications, as the whole data set is usually too large to be fit into memory in practice. However, compared to the offline algorithms, the existing streaming algorithms for submodular maximization generally have weaker capabilities in that they handle more limited problem constraints or achieve weaker performance bounds, due to the more stringent requirements under the streaming setting. Another classification of the existing algorithms is that they concentrate on either monotone or non-monotone submodular functions. As monotone submodular function is a special case of non-monotone submodular function, we will concentrate on non-monotone submodular maximization in this paper.

Energy Constrained Sum-Rate Maximization in IRS-Assisted UAV Networks With Imperfect Channel Information

The focus of this work is maximizing the sum-rate of wireless unmanned aerial vehicle (UAV) networks with intelligent reflecting surfaces (IRS) in the presence of system practical limitations. More specifically, we consider that the phase compensation at the IRS is imperfect due to various factors such as device imperfections and channel estimation errors. Moreover, we consider that the IRS elements have limited switching frequency, which limits the possibility of being allocated to different UAVs over consecutive time slots when time-division multiple access (TDMA) is considered. To this end, we formulate an optimization problem where the objective is to maximize the network sum-rate subject to total energy and quality-of-service (QoS) constraints by optimizing the number of IRS elements and power allocated to each UAV. To solve the optimization problem, a low-complexity heuristic algorithm is proposed based on the quality of the estimated phase for each IRS element. The proposed approach is compared to benchmark techniques such as the uniform allocation process and genetic algorithm. The obtained results show that a significant sum-rate improvement of up to 45% can be gained using the proposed algorithm.

A general framework for probabilistic sensitivity analysis with respect to distribution parameters

Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity measures, including information theoretical metrics such as the Fisher information. The framework is derived analytically via a constrained maximisation and the sensitivity analysis is reformulated into an eigenvalue problem. There are only two main steps to implement the sensitivity framework utilising the likelihood ratio/score function method, a Monte Carlo type sampling followed by solving an eigenvalue equation. The resulting eigenvectors then provide the directions for simultaneous variations of the input parameters and guide the focus to perturb uncertainty the most. Not only is it conceptually simple, but numerical examples demonstrate that the proposed framework also provides new sensitivity insights, such as the combined sensitivity of multiple correlated uncertainty metrics, robust sensitivity analysis with an entropic constraint, and approximation of deterministic sensitivities. Three different examples, ranging from a simple cantilever beam to an offshore marine riser, are used to demonstrate the potential applications of the proposed sensitivity framework to applied mechanics problems.

Revisiting PGD Attacks for Stability Analysis of High-Dimensional Nonlinear Systems and Perception-Based Control

Many existing region-of-attraction (ROA) analysis tools find difficulty in addressing feedback systems with large-scale neural network (NN) policies and/or high-dimensional sensing modalities such as cameras. In this letter, we tailor the projected gradient descent (PGD) attack method as a general-purpose ROA analysis tool for high-dimensional nonlinear systems and end-to-end perception-based control. We show that the ROA analysis can be approximated as a constrained maximization problem such that PGD-based iterative methods can be directly applied. In the model-based setting, we show that the PGD updates can be efficiently performed using back-propagation. In the model-free setting, we propose a finite-difference PGD estimate which is general and only requires a black-box simulator for generating the trajectories of the closed-loop system given any initial state. Finally, we demonstrate the scalability and generality of our analysis tool on several numerical examples with large state dimensions or complex image observations.

Streaming Algorithms for Constrained Submodular Maximization

It is of great importance to design streaming algorithms for submodular maximization, as many applications (e.g., crowdsourcing) have large volume of data satisfying the well-known ''diminishing returns'' property, which cannot be handled by offline algorithms requiring full access to the whole dataset. However, streaming submodular maximization has been less studied than the offline algorithms due to the hardness brought by more stringent requirements on memory consumption. In this paper, we consider the fundamental problem of Submodular Maximization under k -System and d -Knapsack constraints (SMSK), which has only been successfully addressed by offline algorithms in previous studies, and we propose the first streaming algorithm for it with provable performance bounds. Our approach adopts a novel algorithmic framework dubbed MultiplexGreedy , making it also perform well under a single k -system constraint. For the special case of SMSK with only d -knapsack constraints, we further propose a streaming algorithm with better performance ratios than the state-of-the-art algorithms. As the SMSK problem generalizes most of the major problems studied in submodular maximization, our algorithms have wide applications in big data processing.

Greedy is Good: Constrained Non-submodular Function Maximization via Weak Submodularity

Greedy is Good: Constrained Non-submodular Function Maximization via Weak Submodularity

Consistent and flexible thermodynamics in atmospheric models using internal energy as a thermodynamic potential. Part I: Equilibrium regime

Approximations in the moist thermodynamics of atmospheric models can often be inconsistent; different parts of numerical models may handle the thermodynamics in different ways, or the approximations may disagree with the laws of thermodynamics. To address these problems, all relevant thermodynamic quantities may be derived from a defined thermodynamic potential; approximations are instead made to the potential itself—this guarantees self‐consistency, as well as flexibility. Previous work showed that this concept is viable for vapour and liquid water mixtures in a moist atmospheric system using the Gibbs potential. However, on extension to include the ice phase, an ambiguity is encountered at the triple point. To resolve this ambiguity, here the internal energy is used instead. Constrained maximisation methods on the entropy can then be used to solve for the system equilibrium state. Nevertheless, a further extension is necessary for realistic atmospheric systems, where many importantnon‐equilibriumprocesses take place; for example, freezing of supercooled water and evaporation into subsaturated air. To capture processes such as these fully, the equilibrium method must be reformulated to involve finite rates of approach towards equilibrium. Here the principles of non‐equilibrium thermodynamics are used, beginning with a set of phenomenological equations, to show how non‐equilibrium moist processes may be coupled to a semi‐implicit semi‐Lagrangian dynamical core. Standard bubble test cases and simulations of idealised cloudy thermals are presented to demonstrate the viability of the approach for the equilibrium regime. Further details and results for non‐equilibrium regimes are presented in Part II.

Fast Adaptive Non-Monotone Submodular Maximization Subject to a Knapsack Constraint

Constrained submodular maximization problems encompass a wide variety of applications, including personalized recommendation, team formation, and revenue maximization via viral marketing. The massive instances occurring in modern-day applications can render existing algorithms prohibitively slow. Moreover, frequently those instances are also inherently stochastic. Focusing on these challenges, we revisit the classic problem of maximizing a (possibly non-monotone) submodular function subject to a knapsack constraint. We present a simple randomized greedy algorithm that achieves a 5.83-approximation and runs in O(n log n) time, i.e., at least a factor n faster than other state-of-the-art algorithms. The versatility of our approach allows us to further transfer it to a stochastic version of the problem. There, we obtain a (9 + ε)-approximation to the best adaptive policy, which is the first constant approximation for non-monotone objectives. Experimental evaluation of our algorithms showcases their improved performance on real and synthetic data.

Effective Approximation Methods for Constrained Utility Maximization with Drift Uncertainty

In this paper, we propose a novel and effective approximation method for finding the value function for general utility maximization with closed convex control constraints and partial information. Using the separation principle and the weak duality relation, we transform the stochastic maximum principle of the fully observable dual control problem into an equivalent error minimization stochastic control problem and find the tight lower and upper bounds of the value function and its approximate value. Numerical examples show the goodness and usefulness of the proposed method.

Explanation guided cross-modal social image clustering

The integration of visual and semantic information has been found to play a role in increasing the accuracy of social image clustering methods. However, existing approaches are limited by the heterogeneity gap between the visual and semantic modalities, and their performances significantly degrade due to the commonly sparse and incomplete tags in semantic modality. To address these problems, we propose a novel clustering framework to discover reasonable categories in unlabeled social images under the guidance of human explanations. First of all, a novel Explanation Generation Model (EGM) is proposed to automatically boost textual information for the sparse and incomplete tags based on an extra lexical database with human knowledge. Then, a novel clustering algorithm called Group Constrained Information Maximization (GCIM) is proposed to learn image categories. In this algorithm, a new type of constraint named group level side information is unprecedentedly defined to bridge the well-known heterogeneity gap between visual and textual modalities. Finally, an interactive draw-and-merge optimization method is proposed to ensure an optimal solution. Extensive experiments on several social image datasets including NUS-Wide, IAPRTC, MIRFlickr, ESP-Game and COCO demonstrate the superiority of the proposed approach to state-of-the-art baselines.

Nonsubmodular Constrained Profit Maximization in Attribute Networks

The number of social individuals who interact with their friends through social networks is increasing, leading to an undeniable fact that word-of-mouth marketing has become one of the useful ways to promote sale of products. The Constrained Profit Maximization in Attribute network (CPMA) problem, as an extension of the classical influence maximization problem, is the main focus of this paper. We propose the profit maximization in attribute network problem under a cardinality constraint which is closer to the actual situation. The profit spread metric of CPMA calculates the total benefit and cost generated by all the active nodes. Different from the classical Influence Maximization problem, the influence strength should be recalculated according to the emotional tendency and classification label of nodes in attribute networks. The profit spread metric is no longer monotone and submodular in general. Given that the profit spread metric can be expressed as the difference between two submodular functions and admits a DS decomposition, a three-phase algorithm named as Marginal increment and Community-based Prune and Search(MCPS) Algorithm frame is proposed which is based on Louvain algorithm and logistic function. Due to the method of marginal increment, MPCS algorithm can compute profit spread more directly and accurately. Experiments demonstrate the effectiveness of MCPS algorithm.

Modeling of a bio-inspired soft arm with semicircular cross section for underwater grasping

Fluid-filled fiber-reinforced elastomeric enclosures (FREEs) with a circular cross section, inspired by the muscle structure of octopus arms, are a popular choice for actuators because of their high power density and relatively low manufacturing cost. However, the shape, flexibility, and grasping force of FREEs are slightly different from those of real octopus arms. A soft arm with a semicircular cross section has better bending performance than that of FREEs with a circular cross section and can thus more easily achieve flexible grasping. In this paper, to better describe the deformation of soft arm shape in an underwater environment, a model based on a constrained maximization volume is proposed for a semicylindrical soft arm. In particular, the model takes into account the effect of the expansion of the bottom on the semicylindrical soft arm and the proposed analytical model is used to analyze the factors that affect the helix radius of the soft arm, including the helix angles of the fibers, wall thickness, and inner radius of the soft arm. Then a method for fabricating soft arms with a semicircular cross section (length: 700 mm) and a method for extracting the helix radius are also proposed. Finally, a series of driving experiments is performed to measure the accuracy of the model using a hydraulic platform. Experimental results show that the maximum error rate of the helix radius is between 8.99% and 12.29%. The helix radius can be varied from 74.3 mm to 176 mm by changing the parameters of the soft arm.