Bounds for the Minimum Distance and Covering Radius of Orthogonal Arrays via Their Distance Distributions

We propose two methods for obtaining estimations on the minimum distance and covering radius of orthogonal arrays. Both methods are based on knowledge about the (feasible) sets of distance distributions of orthogonal arrays with given length, cardinality, factors and strength. New bounds are presented either in analytic form and as products of an ongoing project for computation and investigation of the possible distance distributions of orthogonal arrays with parameters in doable ranges.

Formalizing Clientelism in Kenya: From Harambee to the Constituency Development Fund

Why does clientelism persist? What determines how politicians signal responsiveness to voters and exert effort towards fulfilling campaign promises? This article explores how state capacity, legislative institutional strength, and established ideas about what politicians can do structure the political market in legislative elections. The argument herein is that campaign promises must be credible to have any currency. Therefore, programmatic campaign promises are likely to be more credible in countries with strong states and legislatures, while clientelism predominates in weak states whose legislatures cannot compel the executive branch to implement legislators’ campaign promises. Historical experience also matters in shaping shared expectations of what politicians can do and the feasible sets of credible campaign promises. I support these arguments with a historical institutionalist analysis of Kenya’s Harambee Movement and the Constituency Development Fund (CDF), as well as evidence from a nationally representative survey. Findings corroborate the claim that clientelism persists when it is the most credible means of fulfilling campaign promises. This article also shows that rising costs can precipitate legislative reforms away from clientelism – as happened with the creation of Kenya’s CDF in 2003. Overall, this article increases our understanding of the origins and persistence of clientelism in low-income states and potential avenues for reform towards programmatic politics.

An explicit extragradient algorithm for solving variational inequality problem with application

In this paper, we introduce a new explicit extragradient algorithm for solving Variational Inequality Problem (VIP) in Banach spaces. The proposed algorithm uses a linesearch method whose inner iterations are independent of any projection onto feasible sets. Under standard and mild assumption of pseudomonotonicity and uniform continuity of the VIP associated operator, we establish the strong convergence of the scheme. Further, we apply our algorithm to find an equilibrium point with minimal environmental cost for a model in electricity production. Finally, a numerical result is presented to illustrate the given model. Our result extends, improves and unifies other related results in the literature.

A parameter-free unconstrained reformulation for nonsmooth problems with convex constraints

In the present paper we propose to rewrite a nonsmooth problem subjected to convex constraints as an unconstrained problem. We show that this novel formulation shares the same global and local minima with the original constrained problem. Moreover, the reformulation can be solved with standard nonsmooth optimization methods if we are able to make projections onto the feasible sets. Numerical evidence shows that the proposed formulation compares favorably against state-of-art approaches. Code can be found at https://github.com/jth3galv/dfppm.

Continuous and Binary Sets of Responses are Not the Same: Evidence from the Field

This paper conducts a pre-registered study aimed to compare binary and continuous set of responses in questionnaires. Binary responses consist of two possible opposed responses (Yes/No). Continuous are numerical, where respondents can indicate an answer in a 0 to 10 horizontal blind line. We study whether binary and continuous feasible sets of responses yield to the same outcome (distribution) and the same cost (duration in minutes). We collect data from 360 households in Honduras who were randomly assigned to Yes/No questions or given a slider (visual scaling 0-10) to mark their responses, therefore, we provide causal evidence. We find that respondents are 13% more likely to say “Yes” and spend 2.1 minutes less in the binary setting. Besides, we find that most of the differences between binary and continuous settings arise from questions which include negative wording.

Continuous and binary sets of responses are not the same: Evidence from the field

This paper conducts a pre-registered study aimed to compare binary and continuous set of responses in questionnaires. Binary responses consist of two possible opposed responses (Yes/No). Continuous are numerical, where respondents can indicate an answer in a 0 to 10 horizontal blind line. We study whether binary and continuous feasible sets of responses yield to thesame outcome (distribution) and the same cost (duration in minutes). We collect data from 360 households in Honduras who were randomly assigned to Yes/No questions or given a slider (visual scaling 0-10) to mark their responses, therefore, we provide causal evidence. We find that respondents are 13% more likely to say “Yes” and spend 2.1 minutes less in the binary setting. Besides, we find that most of the differences between binary and continuous settings arise from questions which include negative wording.

Information Aggregation for Constrained Online Control

This paper considers an online control problem involving two controllers. A central controller chooses an action from a feasible set that is determined by time-varying and coupling constraints, which depend on all past actions and states. The central controller's goal is to minimize the cumulative cost; however, the controller has access to neither the feasible set nor the dynamics directly, which are determined by a remote local controller. Instead, the central controller receives only an aggregate summary of the feasibility information from the local controller, which does not know the system costs. We show that it is possible for an online algorithm using feasibility information to nearly match the dynamic regret of an online algorithm using perfect information whenever the feasible sets satisfy a causal invariance criterion and there is a sufficiently large prediction window size. To do so, we use a form of feasibility aggregation based on entropic maximization in combination with a novel online algorithm, named Penalized Predictive Control (PPC) and demonstrate that aggregated information can be efficiently learned using reinforcement learning algorithms. The effectiveness of our approach for closed-loop coordination between central and local controllers is validated via an electric vehicle charging application in power systems.

Optimality conditions for nonconvex problems over nearly convex feasible sets

In this paper, we study the optimization problem (P) of minimizing a convex function over a constraint set with nonconvex constraint functions. We do this by given new characterizations of Robinson’s constraint qualification, which reduces to the combination of generalized Slater’s condition and generalized sharpened nondegeneracy condition for nonconvex programming problems with nearly convex feasible sets at a reference point. Next, using a version of the strong CHIP, we present a constraint qualification which is necessary for optimality of the problem (P). Finally, using new characterizations of Robinson’s constraint qualification, we give necessary and sufficient conditions for optimality of the problem (P).

Heterogeneous Choice Sets and Preferences

We propose a robust method of discrete choice analysis when agents' choice sets are unobserved. Our core model assumes nothing about agents' choice sets apart from their minimum size. Importantly, it leaves unrestricted the dependence, conditional on observables, between choice sets and preferences. We first characterize the sharp identification region of the model's parameters by a finite set of conditional moment inequalities. We then apply our theoretical findings to learn about households' risk preferences and choice sets from data on their deductible choices in auto collision insurance. We find that the data can be explained by expected utility theory with low levels of risk aversion and heterogeneous non‐singleton choice sets, and that more than three in four households require limited choice sets to explain their deductible choices. We also provide simulation evidence on the computational tractability of our method in applications with larger feasible sets or higher‐dimensional unobserved heterogeneity.