In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: Encoding finite linear CSPs as Boolean formulas and solving them by using modern SAT solvers has proven to be highly effective, as exemplified by the award-winning sugar system. We here develop an alternative approach based on ASP. This allows us to use first-order encodings providing us with a high degree of flexibility for easy experimentation with different implementations. The resulting system aspartame re-uses parts of sugar for parsing and normalizing CSPs. The obtained set of facts is then combined with an ASP encoding that can be grounded and solved by off-the-shelf ASP systems. We establish the competitiveness of our approach by empirically contrasting aspartame and sugar.

A: Aspartame: Solving Constraint Satisfaction Problems with Answer Set Programming
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Q: The Augmented Lagragian Method (ALM) and Alternating Direction Method of Multiplier (ADMM) have been powerful optimization methods for general convex programming subject to linear constraint. We consider the convex problem whose objective consists of a smooth part and a nonsmooth but simple part. We propose the Fast Proximal Augmented Lagragian Method (Fast PALM) which achieves the convergence rate O(1/K), compared with O(1/K) by the traditional PALM. In order to further reduce the per-iteration complexity and handle the multi-blocks problem, we propose the Fast Proximal ADMM with Parallel Splitting (Fast PL-ADMM-PS) method. It also partially improves the rate related to the smooth part of the objective function. Experimental results on both synthesized and real world data demonstrate that our fast methods significantly improve the previous PALM and ADMM. Introduction This work aims to solve the following linearly constrained separable convex problem with n blocks of variables min x1,··· ,xn f(x) = n ∑

A: Fast Proximal Linearized Alternating Direction Method of Multiplier with Parallel Splitting
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Q: In this paper, we provide two axiomatizations of algebraic expected utility, which is a particular generalized expected utility, in a von NeumannMorgenstern setting, i.e. uncertainty representation is supposed to be given and here to be described by a plausibility measure valued on a semiring, which could be partially ordered. We show that axioms identical to those for expected utility entail that preferences are represented by an algebraic expected utility. This algebraic approach allows many previous propositions (expected utility, binary possibilistic utility,...) to be unified in a same general framework and proves that the obtained utility enjoys the same nice features as expected utility: linearity, dynamic consistency, autoduality of the underlying uncertainty representation, autoduality of the decision criterion and possibility of modeling decision maker’s attitude toward uncertainty.

A:
Axiomatic Foundations for a Class of Generalized Expected Utility: Algebraic Expected Utility
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