The automorphism group and the non-self-duality of p-cones

In this paper, we determine the automorphism group of the p-cones (p\neq 2) in dimension greater than two. In particular, we show that the automorphism group of those p-cones are the positive scalar multiples of the generalized permutation matrices that fix the main axis of the cone. Next, we take a look at a problem … Read more

On positive duality gaps in semidefinite programming

We study semidefinite programs (SDPs) with positive duality gaps, i.e., different optimal values in the primal and dual problems. the primal and dual problems differ. These SDPs are considered extremely pathological, they are often unsolvable, and they also serve as models of more general pathological convex programs. We first fully characterize two variable SDPs with … Read more

Strict Complementarity in MaxCut SDP

The MaxCut SDP is one of the most well-known semidefinite programs, and it has many favorable properties. One of its nicest geometric/duality properties is the fact that the vertices of its feasible region correspond exactly to the cuts of a graph, as proved by Laurent and Poljak in 1995. Recall that a boundary point x … Read more

An ADMM-Based Interior-Point Method for Large-Scale Linear Programming

In this paper, we propose a new framework to implement interior point method (IPM) in order to solve some very large scale linear programs (LP). Traditional IPMs typically use Newton’s method to approximately solve a subproblem that aims to minimize a log-barrier penalty function at each iteration. Due its connection to Newton’s method, IPM is … Read more

Polyhedral-based Methods for Mixed-Integer SOCP in Tree Breeding

Optimal contribution selection (OCS) is a mathematical optimization problem that aims to maximize the total benefit from selecting a group of individuals under a constraint on genetic diversity. We are specifically focused on OCS as applied to forest tree breeding, when selected individuals will contribute equally to the gene pool. Since the diversity constraint in … Read more

Distributionally robust optimization with polynomial densities: theory, models and algorithms

In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A common shortcoming of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distribution that give nature too much … Read more

A new approximation algorithm for unrelated parallel machine scheduling problem with release dates

In this research, we consider the unrelated parallel machine scheduling problem with release dates. The goal of this scheduling problem is to find an optimal job assignment with minimal sum of weighted completion times. As it is demonstrated in the present paper, this problem is NP-hard in the strong sense. Albeit the computational complexity, which … Read more

Shortfall Risk Models When Information of Loss Function Is Incomplete

Utility-based shortfall risk measure (SR) has received increasing attentions over the past few years for its potential to quantify more effectively the risk of large losses than conditional value at risk. In this paper we consider the case that the true loss function is unavailable either because it is difficult to be identified or the … Read more

A quadratic penalty algorithm for linear programming and its application to linearizations of quadratic assignment problems

This paper provides the first meaningful documentation and analysis of an established technique which aims to obtain an approximate solution to linear programming problems prior to applying the primal simplex method. The underlying algorithm is a penalty method with naive approximate minimization in each iteration. During initial iterations an approach similar to augmented Lagrangian is … Read more