In this paper, we put forth distributed algorithms for solving loosely coupled unconstrained and constrained optimization problems. Such problems are usually solved using algorithms that are based on a combination of decomposition and first order methods. These algorithms are commonly very slow and require many iterations to converge. In order to alleviate this issue, we propose algorithms that...

The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semide nite programming, and nonconvex and nonlinear problems, have reached varyin...

This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial prog...

This study examines two different barrier functions and their use in both path-following and potential-reduction interior-point algorithms for solving a linear program of the form: minimize cTZ subject to Az = b and e < z < u, where components of e and u can be nonfinite, so the variables z can have 0-, 1-,or 2-sided bounds, j = 1, ..., n. The barrier functions that we study include an extensio...

In this paper, we proposed algorithms interior proximal methods based on entropylike distance for the minimization of the quasiconvex function subjected to nonnegativity constraints. Under the assumptions that the objective function is bounded below and continuously differentiable, we established the well definedness of the sequence generated by the algorithms and obtained two important converg...

We present primal-dual interior-point algorithms with polynomial iteration bounds to nd approximate solutions of semidenite programming problems. Our algorithms achieve the current best iteration bounds and, in every iteration of our algorithms, primal and dual objective values are strictly improved.

Placement of interior node points is a crucial step in the generation of quality meshes in sweeping algorithms. Two new algorithms were devised for node point placement and implemented in Sweep Tool, the first based on the use of linear transformations between bounding node loops and the second based on smoothing. Examples are given that demonstrate the effectiveness of these algorithms.

We explore a preconditioning technique applied to the problem of solving linear systems arising from primal-dual interior point algorithms in linear and quadratic programming. The preconditioner has the attractive property of improved eigenvalue clustering with increased illconditioning of the (1,1) block of the saddle point matrix. It fits well into the optimization framework since the interio...

In this paper we propose a new large-update primal-dual interior point algorithm for P∗(κ) linear complementarity problems (LCPs). We generalize the analysis of BER’s primal-dual interior point algorithm for LP to P∗(κ) LCPs. New search directions and proximity measures are proposed based on a new kernel function which has linear growth term. We showed that if a strictly feasible starting point...