‎we consider nonconvex vector optimization problems with variable ordering structures in banach spaces‎. ‎under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems‎. ‎using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...

When designing controllers with robust performance and stabilization requirements, H-infinity synthesis is a common tool to use. These controllers are often obtained by solving mathematical optimization problems. The controllers that result from these algorithms are typically of very high order, which complicates implementation. Low order controllers are usually desired, since they are consider...

In this paper we investigate the problem of allocating spectrum among radio nodes under SINR requirements. This problem is of special interest in dynamic spectrum access networks where topology and spectral resources differ with time and location. The problem is to determine the number of radio nodes that can transmit simultaneously while still achieving their SINR requirements and then decide ...

Distributed detection over a blockchain-aided Internet of Things (BIoT) network in the presence attacks is considered, where integrated blockchain employed to secure data exchanges BIoT as well storage at agents BIoT. We consider general adversary model attackers jointly exploit vulnerability IoT devices and that The optimal attacking strategy which minimizes Kullback-Leibler divergence pursued...

|ξ| ≤ f(x, u, ξ) ≤ L(1 + |ξ|). A function u ∈ W 1,p loc (Ω) is a local minimizer of F in Ω if F (u; spt (v − u)) ≤ F (v; spt (v − u)) , for every v ∈ W 1,p loc (Ω) such that spt (v − u) ⊂⊂ Ω. Well known results due to Giaquinta and Giusti [13, 15] ensure that local minimizers of F are locally α-Hölder continuous for some α < 1. According to Meyers’ example in [19], when f is not continuous in Ω...

The α-reformulation (αR) technique can be used to transform any nonconvex twice-differentiable mixedinteger nonlinear programming problem to a convex relaxed form. By adding a quadratic function to the nonconvex function it is possible to convexify it, and by subtracting a piecewise linearization of the added function a convex underestimator will be obtained. This reformulation technique is imp...

We propose an optimization framework for nonconvex problems based on majorizationminimization that is particularity well-suited for parallel computing. It reduces the optimization of a high dimensional nonconvex objective function to successive optimizations of locally tight and convex upper bounds which are additively separable into low dimensional objectives. The original problem is then brok...