In this paper we present a new steepest-descent type algorithm for convex optimization problems. Our algorithm pieces the unknown into sub-blocs of unknowns and considers a partial optimization over each sub-bloc. In quadratic optimization, our method involves Newton technique to compute the step-lengths for the sub-blocs resulting descent directions. Our optimization method is fully parallel a...

In many real-life design problems, there is a requirement to simultaneously balance multiple tasks or objectives in the system that are conflicting in nature, where minimizing one objective causes another to increase in value, thereby resulting in trade-offs between the objectives. For example, in embedded multi-core mobile devices and very large scale data centers, there is a continuous proble...

Abstract. In this paper, a modified gradient projection method is proposed to solve the nonlinear constrained optimization problems, where the search direction is obtained by combing feasibility with descent. In addition, it is pointed out that, for linear constrained optimization problems, this method may be simplified and viewed as the modified version to Rosen’s method. The theoretical analy...

The steepest-descent method is a well-known and effective single-objective descent algorithm when the gradient of the objective function is known. Here, we propose a particular generalization of this method to multi-objective optimization by considering the concurrent minimization of n smooth criteria {J i } (i = 1,. .. , n). The novel algorithm is based on the following observation: consider a...

A power calculation is crucial in planning genetic studies. In genetic association studies, the power is often calculated using the expected number of individuals with each genotype calculated from an assumed allele frequency under Hardy-Weinberg equilibrium. Since the allele frequency is often unknown, the number of individuals with each genotype is random and so a power calculation assuming a...

In this paper, We propose a new nonlinear conjugate gradient method (FRA) that satisfies sufficient descent condition and global convergence under the inexact line search of strong wolf powell. Our numerical experiment shaw efficiency in solving set problems from CUTEst package, proposed formula gives excellent results at CPU time, number iterations, ratings when compared to WYL, DY, PRP, FR me...

Any piecewise smooth function that is specified by an evaluation procedure involving smooth elemental functions and piecewise linear functions like min and max can be represented in the so-called abs-normal form. By an extension of algorithmic, or automatic, differentiation, one can then compute certain first and second order derivative vectors and matrices that represent a local piecewise line...

We consider the parallel variable distribution (PVD) approach proposed by Ferris and Mangasarian [SIAM J. Optim., 4 (1994), pp. 815–832] for solving optimization problems. The problem variables are distributed among p processors with each processor having the primary responsibility for updating its block of variables while allowing the remaining “secondary” variables to change in a restricted f...

The space of directed sets is a Banach space in which convex compact subsets of Rn are embedded. Each directed set is visualized as a (nonconvex) subset of Rn, which is comprised of a convex, a concave and a mixed-type part. Following an idea of A. Rubinov, the directed subdifferential of a difference of convex (DC) functions is defined as the directed difference of the corresponding embedded c...

Landing mission concepts that are being developed for exploration of solar system bodies are increasingly ambitious in their implementations and objectives. Most of these missions require accurate position and velocity data during their descent phase in order to ensure safe, soft landing at the pre-designated sites. Data from the vehicle’s Inertial Measurement Unit will not be sufficient due to...