In the paper we propose an algorithm for nding approximate sparse solutions of convex optimization problem with conic constraints and examine convergence properties of the algorithm with application to the index tracking problem and unconstrained l1-penalized regression.

This paper is devoted to studying the robust isolated calmness of the Karush– Kuhn–Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both t...

in this article, an effective method to control a power system during emergency conditions is presented. based on fuzzy linear programming (flp), a new technique is developed to solve the load shedding and generation reallocation (lsgr) optimization problem. the objective function consists of terms of load curtailments and deviations in generation schedules. the constraints are power system var...

this paper presents a fuzzy decision-making approach to deal with a clustering supplier problem in a supply chain system. during recent years, determining suitable suppliers in the supply chain has become a key strategic consideration. however, the nature of these decisions is usually complex and unstructured. in general, many quantitative and qualitative factors, such as quality, price, and fl...

in recent years, soft computing methods have generated a large research interest. the synthesis of the fuzzy logic and the evolutionary algorithms is one of these methods. a particular evolutionary algorithm (ea) is differential evolution (de). as for any ea, de algorithm also requires parameters tuning to achieve desirable performance. in this paper tuning the perturbation factor vector of de ...

In this paper, we consider a stochastic Time-Cost Tradeoff Problem (TCTP) in PERT networks for project management, in which all activities are subjected to a linear cost function and assumed to be exponentially distributed. The aim of this problem is to maximize the project completion probability with a pre-known deadline to a predefined probability such that the required additional cost is min...

A Real-Time Optimization (RTO) strategy incorporating the fuzzy sets theory is developed, where the problem constraints obtained from process considerations are treated in fuzzy environment. Furthermore, the objective function is penalized by a fuzzified form of the key process constraints. To enable using conventional optimization techniques, the resulting fuzzy optimization problem is the...

Yuan’s theorem of the alternative is an important theoretical tool in optimization, which provides a checkable certificate for the infeasibility of a strict inequality system involving two homogeneous quadratic functions. In this paper, we provide a tractable extension of Yuan’s theorem of the alternative to the symmetric tensor setting. As an application, we establish that the optimal value of...

We investigate the derivation of disjunctive conic cuts for mixed integer second order cone optimization (MISOCO). These conic cuts characterize the convex hull of the intersection of a disjunctive set and the feasible set of a MISOCO problem. We present a full characterization of these inequalities when the disjunctive set considered is defined by parallel hyperplanes.

This paper studies several classes of nonconvex optimization problems defined over convex cones, establishing connections between them and demonstrating that they can be equivalently formulated as convex completely positive programs. The problems being studied include: a conic quadratically constrained quadratic program (QCQP), a conic quadratic program with complementarity constraints (QPCC), ...