It is an open question whether there is an interior-point algorithm for linear optimization problems with a lower iteration-complexity than the classical bound O( √ n log(1 μ0 )). This paper provides a negative answer to that question for a variant of the Mizuno-Todd-Ye predictor-corrector algorithm. In fact, we prove that for any > 0, there is a redundant Klee-Minty cube for which the aforemen...

In this paper, we give a unified analysis for both largeand small-update interior-point methods for the Cartesian P∗(κ )-linear complementarity problem over symmetric cones based on a finite barrier. The proposed finite barrier is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center for the algorithm. The symmetry of the result...

Based on the block compressed sensing (BCS) framework, a new and non-orthogonal transform named all phase biorthogonal transform (APBT) is introduced to exploit the image sparsity, reduce the encoding complexity and be applicable to the blocked image easily. APBT exploits the signal sparsity better than DCT, and meanwhile it overcomes the defects of multiscale transform such as wavelet transfor...

A first order affine scaling method and two mth order affine scaling methods for solving monotone linear complementarity problems (LCP) are presented. All three methods produce iterates in a wide neighborhood of the central path. The first order method has O(nL2(lognL2)(log lognL2)) iteration complexity. If the LCP admits a strict complementary solution then both the duality gap and the iterati...

In this paper, a multilevel successive iteration method for solving nonlinear elliptic problems is proposed by combining a multilevel linearization technique and the cascadic multigrid approach. The error analysis and the complexity analysis for the proposed method are carried out based on the two-grid theory and its multilevel extension. A superconvergence result for the multilevel linearizati...

Signal processing applications which are iterative in nature are best represented by data flow graphs (DFG). In these applications, the maximum sampling frequency is dependent on the topology of the DFG, the cyclic dependencies in particular. The determination of the iteration bound, which is the reciprocal of the maximum sampling frequency, is critical in the process of hardware implementation...

In this paper, we analyze the iteration-complexity of Generalized Forward–Backward (GFB) splitting algorithm, as proposed in [2], for minimizing a large class of composite objectives f` řn i“1 hi on a Hilbert space, where f has a Lipschitzcontinuous gradient and the hi’s are simple (i.e. their proximity operators are easy to compute). We derive iterationcomplexity bounds (pointwise and ergodic)...

Growth in colonial organisms by iteration of modules inherently provides for an increase in available morpho-ecospace relative to their solitary relatives. Therefore, the interpretation of the functional or evolutionary significance of complexity within groups that exhibit modular growth may need to be considered under criteria modified from those used to interpret complexity in solitary organi...

This paper considers a special but broad class of convex programming (CP) problems whose feasible region is a simple compact convex set intersected with the inverse image of a closed convex cone under an affine transformation. It studies the computational complexity of quadratic penalty based methods for solving the above class of problems. An iteration of these methods, which is simply an iter...

Nonconvex optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology. A reason for this relatively low degree of popularity is the lack of a well developed system of theory and algorithms to support the applications, as is the case for its convex counterpart. This paper aims to take one step i...