In this study, a convex proximal point algorithm (CPPA) is considered for solving constrained non-convex problems, and new theoretical results are proposed. It proved that every cluster of CPPA stationary point, the initial key to global optimization. Several sufficient conditions selection provided find minimum. Motivated by these results, numerical experiments were conducted on quadratic prog...

Motivated by recent increased interest in optimization algorithms for non-convex application to training deep neural networks and other problems data analysis, we give an overview of theoretical results on global performance guarantees optimization. We start with classical arguments showing that general could not be solved efficiently a reasonable time. Then list can find the minimizer exploiti...

We lower bound the complexity of finding $$\epsilon $$ -stationary points (with gradient norm at most ) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased oracle with bounded variance, we prove that (in worst case) any algorithm requires least ^{-4}$$ find point. The is tight, and establis...

This paper proposes a constrained stochastic successive convex approximation (CSSCA) algorithm to find a stationary point for a general non-convex stochastic optimization problem, whose objective and constraint functions are nonconvex and involve expectations over random states. The existing methods for non-convex stochastic optimization, such as the stochastic (average) gradient and stochastic...

We propose an alternative method for computing e¤ectively the solution of the control inventory problem under non-convex polynomial cost functions. We apply the method of moments in global optimization to transform the corresponding, non-convex dynamic programming problem into an equivalent optimal control problem with linear and convex structure. We device computational tools based on convex o...

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and admit significantly less efficient algorithms. This motivates the computation...

  The clustering problem under the criterion of minimum sum of squares is a non-convex and non-linear program, which possesses many locally optimal values, resulting that its solution often falls into these trap and therefore cannot converge to global optima solution. In this paper, an efficient hybrid optimization algorithm is developed for solving this problem, called Tabu-KM. It gathers the ...

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...