The purpose of this paper is two-fold. Firstly, we show that every Cholesky-based weighted central path for semidefinite programming is analytic under strict complementarity. This result is applied to homogeneous cone programming to show that the central paths defined by the known class of optimal self-concordant barriers are analytic in the presence of strictly complementary … Read more
The generalized mean function has been widely used in convex analysis and mathematical programming. This paper studies a further generalization of such a function. A necessary and sufficient condition is obtained for the convexity of a generalized function. Additional sufficient conditions that can be easily checked are derived for the purpose of identifying some classes … Read more
We analyze the problem of finding a point strictly interior to a bounded, fully dimensional set from a finite dimensional Hilbert space. We generalize the results obtained for the LP, SDP and SOCP cases. The cuts added by our algorithm are central and conic. In our analysis, we find an upper bound for the number … Read more
We obtain a class of primal ane scaling algorithms which generalize some known algorithms. This class, depending on a r-parameter, is constructed through a family of metrics generated by ��r power, r 1, of the diagonal iterate vector matrix. We prove the so-called weak convergence of the primal class for nondegenerate linearly constrained convex … Read more
One of the fundamental clustering problems is to assign $n$ points into $k$ clusters based on the minimal sum-of-squares(MSSC), which is known to be NP-hard. In this paper, by using matrix arguments, we first model MSSC as a so-called 0-1 semidefinite programming (SDP). We show that our 0-1 SDP model provides an unified framework for … Read more
In [1] several conditions are described which imply the closedness of linear images of convex sets. Here we combine two such theorems into a common generalization. We give a proof of the general theorem which is simpler than the proof obtained by combining the proofs of the two theorems. The paper is almost self-contained as … Read more
We propose a perturbed gradient algorithm with stochastic noises to solve a general class of optimization problems. We provide a convergence proof for this algorithm, under classical assumptions on the descent direction, and new assumptions on the stochastic noises. Instead of requiring the stochastic noises to correspond to martingale increments, we only require these noises … Read more
For a real world problem — transporting pallets between warehouses in order to guarantee sufficient supply for known and additional stochastic demand — we propose a solution approach via convex relaxation of an integer programming formulation, suitable for online optimization. The essential new element linking routing and inventory management is a convex piecewise linear cost … Read more
A wide variety of problems in global optimization, combinatorial optimization as well as systems and control theory can be solved by using linear and semidefinite programming. Sometimes, due to the use of floating point arithmetic in combination with ill-conditioning and degeneracy, erroneous results may be produced. The purpose of this article is to show how … Read more
The inclusion of transaction costs is an essential element of any realistic portfolio optimization. In this paper, we consider an extension of the standard portfolio problem in which convex transaction costs are incurred to rebalance an investment portfolio. In particular, we consider linear, piecewise linear, and quadratic transaction costs. The Markowitz framework of mean-variance efficiency … Read more