A complexity theory for feasible closure properties

A Complexity Theory for Feasible Closure Properties

The study of the complexity of sets encompasses two complementary aims: (1) establishing-usually via explicit construction of algorithms-that sets are feasible, and (2) studying the relative complexity of sets that plausibly might be feasible but are not currently known to be feasible (such as the NP-complete sets and the PSPACE-complete sets ). For the study of the complexity of closure proper...

Complexity Theory and Bounded Arithmetic for Truly Feasible Computation

A Feasible Theory for Analysis

We construct a weak second-order theory of arithmetic which includes Weak König’s Lemma (WKL) for trees defined by bounded formulae. The provably total functions (with Σ1-graphs) of this theory are the polynomial time computable functions. It is shown that the first-order strength of this version of WKL is exactly that of the scheme of collection for bounded formulae.

Iteration Complexity of Feasible Descent Methods Iteration Complexity of Feasible Descent Methods for Convex Optimization

In many machine learning problems such as the dual form of SVM, the objective function to be minimized is convex but not strongly convex. This fact causes difficulties in obtaining the complexity of some commonly used optimization algorithms. In this paper, we proved the global linear convergence on a wide range of algorithms when they are applied to some non-strongly convex problems. In partic...

Quantified Constraint Satisfaction Problems: Closure Properties, Complexity, and Algorithms

There has been much prior work on understanding the complexity of the constraint satisfaction problem (CSP), a broad framework capturing many combinatorial problems. This paper studies the complexity of the quantified constraint satisfaction problem (QCSP), a natural and strict generalization of the CSP. The CSP can be viewed as the problem of deciding whether or not existentially quantified fo...