Conic relaxation approaches for equal deployment problems

An important problem in the breeding of livestock, crops, and forest trees is the optimum of selection of genotypes that maximizes genetic gain. The key constraint in the optimal selection is a convex quadratic constraint that ensures genetic diversity, therefore, the optimal selection can be cast as a second-order cone programming (SOCP) problem. Yamashita et … Read more

A Successive LP Approach with C-VaR Type Constraints for IMRT Optimization

Radiation therapy is considered to be one of important treatment protocols for cancers. Radiation therapy employs several beams of ionizing radiation to kill cancer tumors, but such irradiation also causes damage to normal tissues. Therefore, a treatment plan should satisfy dose-volume constraints (DVCs). Intensity-modulated radiotherapy treatment (IMRT) enables to control the beam intensities and gives … Read more

An efficient second-order cone programming approach for optimal selection in tree breeding

An important problem in tree breeding is optimal selection from candidate pedigree members to produce the highest performance in seed orchards, while conserving essential genetic diversity. The most beneficial members should contribute as much as possible, but such selection of orchard parents would reduce performance of the orchard progeny due to serious inbreeding. To avoid … Read more

A trust-region method for box-constrained nonlinear semidefinite programs

We propose a trust-region method for nonlinear semidefinite programs with box-constraints. The penalty barrier method can handle this problem, but the size of variable matrices available in practical time is restricted to be less than 500. We develop a trust-region method based on the approach of Coleman and Li (1996) that utilizes the distance to … Read more

Fast implementation for semidefinite programs with positive matrix completion

Solving semidefinite programs (SDP) in a short time is the key to managing various mathematical optimization problems in practical time. The matrix-completion primal-dual interior-point method (MC-PDIPM) extracts a structural sparsity of input SDP by factorizing the variable matrices, and it shrinks the computation time. In this paper, we propose a new factorization based on the … Read more

Parallel Implementation of Successive Sparse SDP Relaxations for Large-scale Euclidean Distance Geometry Problems

The Euclidean distance geometry problem (EDGP) includes locating sensors in a sensor network and constructing a molecular configuration using given distances in the two or three-dimensional Euclidean space. When the locations of some nodes, called anchors, are given, the problem can be dealt with many existing methods. An anchor-free problem in the three-dimensional space, however, … Read more

Correlative Sparsity Structures and Semidefinite Relaxations for Concave Cost Transportation Problems with Change of Variables

We present a hierarchy of semidefinite programming (SDP) relaxations for solving the concave cost transportation problem (CCTP), which is known to be NP-hard, with $p$ suppliers and $q$ demanders. In particular, we study cases in which the cost function is quadratic or square-root concave. The key idea of our relaxation methods is in the change … Read more

Parallel solver for semidefinite programming problem having sparse Schur complement matrix

SemiDefinite Programming (SDP) problem is one of the most central problems in mathematical programming. SDP provides a practical computation framework for many research fields. Some applications, however, require solving large-scale SDPs whose size exceeds the capacity of a single processor in terms of computational time and available memory. SDPARA (SemiDefinite Programming Algorithm paRAllel version) developed … Read more

A high-performance software package for semidefinite programs: SDPA 7

The SDPA (SemiDefinite Programming Algorithm) Project launched in 1995 has been known to provide high-performance packages for solving large-scale Semidefinite Programs (SDPs). SDPA Ver. 6 solves efficiently large-scale dense SDPs, however, it required much computation time compared with other software packages, especially when the Schur complement matrix is sparse. SDPA Ver. 7 is now completely … Read more

Enclosing Ellipsoids and Elliptic Cylinders of Semialgebraic Sets and Their Application to Error Bounds in Polynomial Optimization

This paper is concerned with a class of ellipsoidal sets (ellipsoids and elliptic cylinders) in the m-dimensional Euclidean space which are determined by a freely chosen positive semidefinite matrix. All ellipsoidal sets in this class are similar to each other through a parallel transformation and a scaling around their centers by a constant factor. Based … Read more