None of the available minimizers for 2-level hazard-free logic minimization can synthesize very large circuits. This limitation has forced researchers to resort to manual and automated circuit partitioning techniques. This paper introduces two new 2-level logic minimizers: Espresso-HF, a heuristic method which is loosely based on Espresso-II, and Impymin, an exact method based on implicit data ...

A min-max formula is proved for the minimum of an integer-valued separable discrete convex function in which taken over set integral elements a box total dual polyhedron. One variant theorem uses notion conjugate (a fundamental concept nonlinear optimization), but we also provide another version that avoids conjugates, and its spirit conceptually closer to standard form classic theorems combina...

The reconstruction from sparse-view projections is one of important problems in computed tomography (CT) limited by the availability or feasibility of obtaining of a large number of projections. Traditionally, convex regularizers have been exploited to improve the reconstruction quality in sparse-view CT, and the convex constraint in those problems leads to an easy optimization process. However...

This paper extends the full convergence of the proximal point method with Riemannian, Semi-Bregman and Bregman distances to solve minimization problems on Hadamard manifolds. For the unconstrained problem, under the assumptions that the optimal set is nonempty and the objective function is continuous and either quasiconvex or satisfies a generalized Lojasiewicz property, we prove the full conve...

The scenario approach is a general data-driven algorithm to chance-constrained optimization. It seeks the optimal solution that feasible carefully chosen number of scenarios. A crucial step in compute cardinality essential sets, which smallest subset scenarios determine solution. This article addresses challenge efficiently identifying sets. For convex problems, we demonstrate sparsest dual pro...

In regularized risk minimization, the associated optimization problem becomes particularly difficult when both the loss and regularizer are nonsmooth. Existing approaches either have slow or unclear convergence properties, are restricted to limited problem subclasses, or require careful setting of a smoothing parameter. In this paper, we propose a continuation algorithm that is applicable to a ...