A vast majority of machine learning algorithms train their models and perform inference by solving optimization problems. In order to capture the learning and prediction problems accurately, structural constraints such as sparsity or low rank are frequently imposed or else the objective itself is designed to be a non-convex function. This is especially true of algorithms that operate in high-di...

in this paper, we deal to obtain some new complexity results for solving semidefinite optimization (sdo) problem by interior-point methods (ipms). we define a new proximity function for the sdo by a new kernel function. furthermore we formulate an algorithm for a primal dual interior-point method (ipm) for the sdo by using the proximity function and give its complexity analysis, and then we sho...

This article presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for class of Itô stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the input by an optimal contraction metric, which greedily minimizes upper bound mean squared tracking error system trajectories. Although probl...

Decision trees usefully represent sparse, high-dimensional, and noisy data. Having learned a function from these data, we may want to thereafter integrate the into larger decision-making problem, for example, picking best chemical process catalyst. We study large-scale, industrially relevant mixed-integer nonlinear nonconvex optimization problem involving both gradient-boosted penalty functions...

Node cooperation can protect wireless networks from eavesdropping by using the physical characteristics of wireless channels rather than cryptographic methods. Allocating the proper amount of power to cooperative nodes is a challenging task. In this paper, we use three cooperative nodes, one as relay to increase throughput at the destination and two friendly jammers to degrade eavesdropper&rsqu...

Many engineering optimization problems frequently encounter continuous variables and discrete variables which adds considerably to the solution complexity. Very few of the existing methods can yield a globally optimal solution when the objective functions are non-convex and non-differentiable. This paper presents a hybrid swarm intelligence approach (HSIA) for solving these nonlinear optimizati...

This paper is devoted to constructing a definite efficient scheme for non-smooth optimization. A separating plane algorithm with additional clipping is proposed. The algorithm is used for solving the unconstrained non-smooth convex optimization problem. The latter problem can be reformulated as the computation of the value of a conjugate function at the origin. The algorithm convergence is prov...