Abstract. We present a line search multigrid method for solving discretized versions of general unconstrained infinite dimensional optimization problems. At each iteration on each level, the algorithm computes either a “direct search” direction on the current level or a “recursive search” direction from coarser level models. Introducing a new condition that must be satisfied by a backtracking l...

There are three main algorithmic techniques for solving constraint satisfaction problems: backtracking search, local search, and dynamic programming. In this chapter, I survey backtracking search algorithms. Algorithms based on dynamic programming [15]— sometimes referred to in the literature as variable elimination, synthesis, or inference algorithms—are the topic of Chapter 7. Local or stocha...

Beam searches are a very effective algorithm for solving problems that prove intractable to complete algorithms like weighted A* and greedy search. Unfortunately, the inadmissible pruning that is the hallmark of a beam search makes the algorithm incomplete. Existing complete extensions to beam search expand pruned nodes systematically according to generation order. Selecting pruned nodes to exp...

In this paper, by combining the splitting method of augmented Lagrange function (ALF) with sequential quadratic programming (SQP) approximation, a novel ALF-based algorithm SQP structure is proposed for multi-block linear constrained nonconvex separable optimization. The new uses idea to decompose original problem into several small-scale subproblems. Meanwhile, approximation and Armijo-type li...

The problem of finding p-harmonic flows arises in a wide range of applications including color image (chromaticity) denoising, micromagnetics, liquid crystal theory, and directional diffusion. In this paper, we propose an innovative curvilinear search method for minimizing p-harmonic energies over spheres. Starting from a flow (map) on the unit sphere, our method searches along a curve that lie...

Multi-Point Constructive Search maintains a small set of “elite solutions” that are used to heuristically guide constructive search through periodically restarting search from an elite solution. Empirical results indicate that for job shop scheduling optimization problems, multi-point constructive search leads to significantly better solutions for equivalent search effort when compared to chron...

In this paper we consider the K-d tree-based backtracking search algorithm and study its performance in the context of vector quantization encoding of speech waveform. We discuss the basic algorithm in detail and highlight the features of optimization as observed from theoretical analysis and from the empirical performance of the backtracking search. It is seen that, despite the 2K dependence o...