Non-convex nested Benders decomposition

We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). We call this algorithm non-convex nested Benders decomposition (NC-NBD). NC-NBD is based on solving dynamically improved mixed-integer linear outer approximations of the MINLP, obtained by piecewise linear relaxations of nonlinear functions. Those MILPs are solved to global optimality using an enhancement of nested Benders decomposition, in which regularization, dynamically refined binary approximations of the state variables and Lagrangian cut techniques are combined to generate Lipschitz continuous non-convex approximations of the value functions. Those approximations are then used to decide whether the approximating MILP has to be dynamically refined and in order to compute feasible solutions for the original MINLP. We prove that NC-NBD converges to an $$\varepsilon $$ ε -optimal solution in a finite number of steps. We provide promising computational results for some unit commitment problems of moderate size.

Nonconcave Utility Maximization with Portfolio Bounds

The problems of nonconcave utility maximization appear in many areas of finance and economics, such as in behavioral economics, incentive schemes, aspiration utility, and goal-reaching problems. Existing literature solves these problems using the concavification principle. We provide a framework for solving nonconcave utility maximization problems, where the concavification principle may not hold, and the utility functions can be discontinuous. We find that adding portfolio bounds can offer distinct economic insights and implications consistent with existing empirical findings. Theoretically, by introducing a new definition of viscosity solution, we show that a monotone, stable, and consistent finite difference scheme converges to the value functions of the nonconcave utility maximization problems. This paper was accepted by Agostino Capponi, finance.

Double Deep Recurrent Reinforcement Learning for Centralized Dynamic Multichannel Access

We consider the problem of dynamic multichannel access for transmission maximization in multiuser wireless communication networks. The objective is to find a multiuser strategy that maximizes global channel utilization with a low collision in a centralized manner without any prior knowledge. Obtaining an optimal solution for centralized dynamic multichannel access is an extremely difficult problem due to the large-state and large-action space. To tackle this problem, we develop a centralized dynamic multichannel access framework based on double deep recurrent Q-network. The centralized node first maps current state directly to channel assignment actions, which can overcome prohibitive computation compared with reinforcement learning. Then, the centralized node can be easy to select multiple channels by maximizing the sum of value functions based on a trained neural network. Finally, the proposed method avoids collisions between secondary users through centralized allocation policy.

Estimates of Generalized Hessians for Optimal Value Functions in Mathematical Programming

We consider the optimal value function of a parametric optimization problem. A large number of publications have been dedicated to the study of continuity and differentiability properties of the function. However, the differentiability aspect of works in the current literature has mostly been limited to first order analysis, with focus on estimates of its directional derivatives and subdifferentials, given that the function is typically nonsmooth. With the progress made in the last two to three decades in major subfields of optimization such as robust, minmax, semi-infinite and bilevel optimization, and their connection to the optimal value function, there is a need for a second order analysis of the generalized differentiability properties of this function. This could enable the development of robust solution algorithms, such as the Newton method. The main goal of this paper is to provide estimates of the generalized Hessian for the optimal value function. Our results are based on two handy tools from parametric optimization, namely the optimal solution and Lagrange multiplier mappings, for which completely detailed estimates of their generalized derivatives are either well-known or can easily be obtained.

On the Online Coalition Structure Generation Problem

We consider the online version of the coalition structure generation problem, in which agents, corresponding to the vertices of a graph, appear in an online fashion and have to be partitioned into coalitions by an authority (i.e., an online algorithm). When an agent appears, the algorithm has to decide whether to put the agent into an existing coalition or to create a new one containing, at this moment, only her. The decision is irrevocable. The objective is partitioning agents into coalitions so as to maximize the resulting social welfare that is the sum of all coalition values. We consider two cases for the value of a coalition: (1) the sum of the weights of its edges, and (2) the sum of the weights of its edges divided by its size. Coalition structures appear in a variety of application in AI, multi-agent systems, networks, as well as in social networks, data analysis, computational biology, game theory, and scheduling. For each of the coalition value functions we consider the bounded and unbounded cases depending on whether or not the size of a coalition can exceed a given value α. Furthermore, we consider the case of a limited number of coalitions and various weight functions for the edges, i.e., unrestricted, positive and constant weights. We show tight or nearly tight bounds for the competitive ratio in each case.

Air-Fluidized Aggregates of Black Soldier fly Larvae

Black soldier fly larvae are a sustainable protein source and play a vital role in the emerging food-waste recycling industry. One of the challenges of raising larvae in dense aggregations is their rise in temperature during feeding, which, if not mitigated, can become lethal to the larvae. We propose applying air-fluidization to circumvent such overheating. However, the behavior of such a system involves complex air-larva interactions and is poorly understood. In this combined experimental and numerical study, we show that the larval activity changes the behavior of the ensemble when compared to passive particles such as dead larvae. Over a cycle of increasing and then decreasing airflow, the states (pressure and height) of the live larva aggregates are single-value functions of the flow speed. In contrast, dead larva aggregates exhibit hysteresis characteristic of traditional fluidized beds, becoming more porous during the ramp down of airflow. This history-dependence for passive particles is supported by simulations that couple agent-based dynamics and computational fluid dynamics. We show that the hysteresis in height and pressure of the aggregates decreases as the activity of simulated larvae increases. To test if air fluidization can increase larval food intake, we performed feeding trials in a fluidization chamber and visualized the food consumption via x-ray imaging. Although the food mixes more rapidly in faster airflow, the consumption rate decreases. Our findings suggest that providing moderate airflow to larval aggregations may alleviate overheating of larval aggregations and evenly distribute the food without reducing feeding rates.