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Proceedings of GO 2005, pp. 237 – 239.New approach to nonconvex constrained optimization ∗Alexander S. StrekalovskyInstitute of System Dynamics and Control Theory, Laboratory of Global Optimization Methods, Lermontov st. 134, Irkutsk,Russia, strekal@icc.ruAbstractKeywords:In this paper we propose new approach based on Global Optimality Conditions for solving continuousnonconvex optimization problems.nonconvex optimization, global optmzality conditions, local search, global search1. IntroductionA huge of optimization problems arising from different application areas are really nonconvexproblems [1]– [3]. The most of such problems deal with (d.c.) functions which can berepresented as a difference of two convex functions.The present situation in Continuous Nonconvex Optimization may be viewed as dominatedby methods transferred from other sciences [1]– [3], as Discrete Optimization (Branch &Bound, cuts methods, outside and inside approximations, vertex enumeration and so on),Physics, Chemistry (simulated annealing methods), Biology (genetic and ant colony algorithms)etc.On the other hand the classical method [7] of convex optimization have been thrown asidebecause of its inefficiency [1]– [6]. As well-known the conspicuous limitation of convex optimizationmethods applied to nonconvex problems is their ability of being trapped at a localextremum or even a critical point depending on a starting point [1]– [3]. So, the classicalapparatus shows itself inoperative for new problems arising from practice.In such a situation it seems very probable to create an approach for finding just a globalsolution to nonconvex problems on one side connected with Convex Optimization Theoryand secondly using the methods of Convex Optimization.Nevertheless we risked to propose such an approach [8] and even to advance the followingprinciples of Nonconvex Optimization.1. The linearization of the basic (generic) nonconvexity of a problem of interest and consequentlya reducing of the problem to a family of (partially) linearized problems.2. The application of convex optimization methods for solving the linearized problemsand, as a consequence, within special local search methods.3. Constructing of "good" (pertinent) approximations (resolving sets) of level surfaces andepigraph boundaries of convex functions.Obviously, the first and the second are rather known. The deepness and effectiveness of thethird may be observed in [8]– [19].∗ This work was supported by RFBR Grant No. 05-01-00110