An inexact successive quadratic approximation method for a class of difference-of-convex optimization problems

In this paper, we propose a new method for a class of difference-of-convex (DC) optimization problems, whose objective is the sum of a smooth function and a possibly non-prox-friendly DC function. The method sequentially solves subproblems constructed from a quadratic approximation of the smooth function and a linear majorization of the concave part of the … Read more

Generalized subdifferentials of spectral functions over Euclidean Jordan algebras

This paper is devoted to the study of generalized subdifferentials of spectral functions over Euclidean Jordan algebras. Spectral functions appear often in optimization problems playing the role of “regularizer”, “barrier”, “penalty function” and many others. We provide formulae for the regular, approximate and horizon subdifferentials of spectral functions. In addition, under local lower semicontinuity, we … Read more

BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems with Binary, Box and Complementarity Constraints

The software package BBCPOP is a MATLAB implementation of a hierarchy of sparse doubly nonnegative (DNN) relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box and complementarity (BBC) constraints. Given a POP in the class and a relaxation order, BBCPOP constructs a simple conic optimization problem (COP), which serves as a … Read more

User Manual for BBCPOP: A Sparse Doubly Nonnegative Relaxation of Polynomial Optimization Problems with Binary, Box and Complementarity Constraints

BBCPOP proposed in [4] is a MATLAB implementation of a hierarchy of sparse doubly nonnegative (DNN) relaxations of a class of polynomial optimization (minimization) problems (POPs) with binary, box and complementarity constraints. Given a POP in the class and a relaxation order (or a hierarchy level), BBCPOP constructs a simple conic optimization problem (COP), which … Read more

Equivalences and Differences in Conic Relaxations of Combinatorial Quadratic Optimization Problems

Various conic relaxations of quadratic optimization problems in nonnega- tive variables for combinatorial optimization problems, such as the binary integer quadratic problem, quadratic assignment problem (QAP), and maximum stable set problem have been proposed over the years. The binary and complementarity conditions of the combi- natorial optimization problems can be expressed in several ways, each … Read more

Exact SDP Relaxations with Truncated Moment Matrix for Binary Polynomial Optimization Problems

For binary polynomial optimization problems (POPs) of degree $d$ with $n$ variables, we prove that the $\lceil(n+d-1)/2\rceil$th semidefinite (SDP) relaxation in Lasserre’s hierarchy of the SDP relaxations provides the exact optimal value. If binary POPs involve only even-degree monomials, we show that it can be further reduced to $\lceil(n+d-2)/2\rceil$. This bound on the relaxation order … Read more

Economic and Environmental Analysis of Photovoltaic Energy Systems via Robust Optimization

This paper deals with the problem of determining the optimal size of a residential grid-connected photovoltaic system to meet a certain CO2 reduction target at a minimum cost. Ren et al. proposed a novel approach using a simple linear programming that minimizes the total energy costs for residential buildings in Japan. However, their approach is … Read more

Simultaneous Pursuit of Out-of-Sample Performance and Sparsity in Index Tracking Portfolios

Index tracking is a passive investment strategy in which an investor purchases a set of assets to mimic a market index. The tracking error, the difference between the performances of the index and the portfolio, may be minimized by buying all the assets contained in the index. However, this strategy results in a considerable amount … Read more

Worst-Case Violation of Sampled Convex Programs for Optimization with Uncertainty

Uncertain programs have been developed to deal with optimization problems including inexact data, i.e., uncertainty. A deterministic approach called robust optimization is commonly applied to solve these problems. Recently, Calafiore and Campi have proposed a randomized approach based on sampling of constraints, where the number of samples is determined so that only small portion of … Read more

On the Role of the Norm Constraint in Portfolio Selection

Recently, several optimization approaches for portfolio selection have been proposed in order to alleviate the estimation error in the optimal portfolio. Among such are the norm-constrained variance minimization and the robust portfolio models. In this paper, we examine the role of the norm constraint in the portfolio optimization from several directions. First, it is shown … Read more