The Conic Benchmark Library (CBLIB 2014) is a collection of more than a hundred conic optimization instances under a free and open license policy. It is the first extensive benchmark library for the advancing field of conic mixed-integer and continuous optimization, which is already supported by all major commercial solvers and spans a wide range of industrial applications. The library addresse...

We consider quadratic programs with a single negative eigenvalue (QP1NE) subject to linear and conic constraints. The QP1NE model covers the classical clique problem that is known to be NP-hard [26]. In this paper, by combining successive linear conic optimization (SLCO), convex relaxation and line search technique, we present a global algorithm for QP1NE which can locate a global optimal solut...

In this study, an environmental economic active power dispatch problem is transformed into an optimization problem with a single-objective function by applying the weighted sum method (WSM) and the conic scalarization method (CSM). A pseudo spot price of electricity algorithm (PSPA) is used to solve the transformed problem. This is demonstrated on an example problem, which is a lossy electrical...

In this paper we consider a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using `1 or `2 norm; with each measure having its advantages and disa...

A Standard Quadratic Optimization Problem (StQP) consists of maximizing a (possibly indefinite) quadratic form over the standard simplex. Likewise, in a multi-StQP we have to maximize a (possibly indefinite) quadratic form over the cartesian product of several standard simplices (of possibly different dimensions). Two converging monotone interior point methods are established. Further, we prove...

For a conic optimization problem P : minimizex c x s.t. Ax = b, x ∈ C and its dual D : supremumy,s b T y s.t. A y + s = c, s ∈ C, we present a geometric relationship between the primal objective function level sets and the dual objective function level sets, which shows that the maximum norms of the primal objective function level sets are nearly inversely proportional to the maximum inscribed ...

In this paper, a special class of redundancy optimization problem with fuzzy random variables is presented. In this model, fuzzy random lifetimes are considered as basic parameters and the Er-expected of system lifetime is used as a major type of system performance. Then a redundancy optimization problem is formulated as a binary integer programming model. Furthermore, illustrative numerical ex...

In this paper we discuss duality theory of optimization problems with a linear objective function and subject to linear constraints with cone inclusions, referred to as conic linear problems. We formulate the Lagrangian dual of a conic linear problem and survey some results based on the conjugate duality approach where the questions of “no duality gap” and existence of optimal solutions are rel...