Solving constrained optimization problems by solution-based decomposition search

Solving constrained optimization problems (COPs) is a challenging task. In this paper we present a new strategy for solving COPs called solve and decompose (or \( S \& D\) for short). The proposed strategy is a systematic iterative depth-first strategy that is based on problem decomposition. \( S \& D\) uses a feasible solution of the COP, found by any exact method, to further decompose the original problem into a bounded number of subproblems which are considerably smaller in size. It also uses the value of the feasible solution as a bound that we add to the created subproblems in order to strengthen the cost-based filtering. Furthermore, the feasible solution is exploited in order to create subproblems that have more promise in finding better solutions which are explored in a depth-first manner. The whole process is repeated until we reach a specified depth where we do not decompose the subproblems anymore but we solve them to optimality using any exact method like Branch and Bound. Our initial results on two benchmark problems show that \( S \& D\) may reach improvements of up to three orders of magnitude in terms of runtime when compared to Branch and Bound.     

Socio‐Emotional Context and Adolescents' Decision Making: The Experience of Regret and Relief After Social Comparison

Many studies indicate that adolescents are hypersensitive to rewards in salient socio‐emotional contexts. However, little is known about adolescents' sensitivity to complex negative emotions. To study the development of the ability to experience regret and relief, children, adolescents, and young adults performed a gambling task in a socio‐emotional context of competition, in which they were informed that their outcome would be compared with that of a competitor. The context of competition impacted the feelings of regret and relief in adolescents. When adolescents experienced an initial negative outcome, their feeling of relief was reinforced. However, they did not seem to experience regret in the social context of competition. These results provide a possible explanation for adolescents' enhanced risk seeking.     

Actor-based analysis of peer influence in A Stop Smoking In Schools Trial (ASSIST)

As shown by the success of network intervention studies that exploit the occurrence of peer influence in their target group, the reliable assessment of peer influence processes can be important for informing public health policy and practice. A recently developed tool for assessing peer influence in longitudinal social network data is stochastic actor-based modeling. The body of the literature in which this method is applied is growing, but how reliable are the results? In this paper, we identify two shortcomings in this literature: the questionable assumption of temporal homogeneity, and the potential dependence of results on the inclusion of nuisance parameters in the model specification. These issues are resolved by analyzing the data of three schools selected from ASSIST, a large UK-based trial of a school-based smoking prevention intervention. Results show that the co-evolution of friendship and smoking is a time heterogeneous process, and that results are sensitive to specification details. However, the peer influence parameter is not affected by either, but emerges as surprisingly stable over time and robust to model variation. This establishes confidence in the method and encourages detailed future investigations of peer influence in ASSIST.     

Peers Increase Late Adolescents' Exploratory Behavior and Sensitivity to Positive and Negative Feedback

Adolescents take more risks with peers than when alone. It is not clear how peer presence affects adolescents' risky decision making, however. We used the Iowa Gambling Task (IGT)—a game used to assess decision making involving risk and reward—to examine how peers affect late adolescents' exploration of relevant environmental cues, ability to learn from the outcomes (positive and negative) of that exploration, and ability to integrate feedback to adjust behavior toward optimal long‐term outcomes. One hundred and one 18‐ to 22‐year old males (M = 19.8 years) were randomly assigned to play the IGT either alone or observed by peers. Late adolescents tested with observers engaged in more exploratory behavior, learned faster from both positive and negative outcomes, and evinced better task performance than those tested alone.     

Optimal income taxation with Kalai wage bargaining and endogenous participation

This paper characterizes the optimal redistributive tax schedule in a search–matching framework where (voluntary) nonparticipation and (involuntary) unemployment are endogenous and wages are determined by proportional bargaining à la Kalai. The optimal employment tax rate is given by an inverse elasticity rule. This rule depends on the global response of the employment rate, which depends not only on the participation (labor supply) responses, but also on the vacancy posting (labor demand) responses and on the product of these two responses. For plausible values of the parameters, our matching environment induces much lower employment tax rates than the usual competitive model with endogenous participation only. However, optimal employment tax rates are larger (in absolute value) when a given level of the global elasticity of employment is more due to search frictions and less due to participation responses.