Combined heat and power dynamic economic emission dispatch (CHPDEED) problem is a complicated nonlinear constrained multiobjective optimization problem with nonconvex characteristics. CHPDEED determines the optimal he...
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Combined heat and power dynamic economic emission dispatch (CHPDEED) problem is a complicated nonlinear constrained multiobjective optimization problem with nonconvex characteristics. CHPDEED determines the optimal heat and power schedule of committed generating units by minimizing both fuel cost and emission simultaneously under ramp rate constraints and other constraints. This paper proposes hybrid differential evolution (DE) and sequential quadratic programming (SQP) to solve the CHPDEED problem with nonsmooth and nonconvex cost function due to valve point effects. DE is used as a global optimizer, and SQP is used as a fine tuning to determine the optimal solution at the final. The proposed hybrid DE-SQP method has been tested and compared to demonstrate its effectiveness.
Under the condition that the values of the objective function and its subgradient are computed approximately, we introduce a cutting plane and level bundle method for minimizing nonsmooth nonconvex functions by combin...
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Under the condition that the values of the objective function and its subgradient are computed approximately, we introduce a cutting plane and level bundle method for minimizing nonsmooth nonconvex functions by combining cutting plane method with the ideas of proximity control and level constraint. The proposed algorithm is based on the construction of both a lower and an upper polyhedral approximation model to the objective function and calculates new iteration points by solving a subproblem in which the model is employed not only in the objective function but also in the constraints. Compared with other proximal bundle methods, the new variant updates the lower bound of the optimal value, providing an additional useful stopping test based on the optimality gap. Another merit is that our algorithm makes a distinction between affine pieces that exhibit a convex or a concave behavior relative to the current iterate. Convergence to some kind of stationarity point is proved under some looser conditions.
We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: -A (x((3)) (t)) is an element of N(K(t, (x) over dot(t));A ((sic)(t))) + F(t, x(...
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We prove the existence of solutions for third-order nonconvex state-dependent sweeping process with unbounded perturbations of the form: -A (x((3)) (t)) is an element of N(K(t, (x) over dot(t));A ((sic)(t))) + F(t, x(t), (x) double over dot(t), (sic)(t)) + G(x(t), (x) over dot(t)), (sic)(t)) a.e. [0, T], A(sic)(t)) is an element of K(t, (x) over dot(t)), a.e. t is an element of [0, T], x(0) = x(0), (x) over dot(0) = u(0), (sic)0 = upsilon(0), where T > 0, K is a nonconvex Lipschitz set-valued mapping, F is an unbounded scalarly upper semicontinuous convex set-valued mapping, and G is an unbounded uniformly continuous nonconvex set-valued mapping in a separable Hilbert space H.
Some properties of the weak subdifferential are considered in this paper. By using the definition and properties of the weak subdifferential which are described in the papers (Azimov and Gasimov, 1999;Kasimbeyli and M...
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Some properties of the weak subdifferential are considered in this paper. By using the definition and properties of the weak subdifferential which are described in the papers (Azimov and Gasimov, 1999;Kasimbeyli and Mammadov, 2009;Kasimbeyli and Inceoglu, 2010), the author proves some theorems connecting weak subdifferential in nonsmooth and nonconvex analysis. It is also obtained necessary optimality condition by using the weak subdifferential in this paper.
We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some...
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We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity. Some special cases are also considered. Our proof of convergence is very simple. Results proved in this paper may stimulate further research in this dynamic field.
By virtue of the separation theorem of convex sets, a necessary condition and a sufficient condition for epsilon-vector equilibrium problem with constraints are obtained. Then, by using the Gerstewitz nonconvex separa...
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By virtue of the separation theorem of convex sets, a necessary condition and a sufficient condition for epsilon-vector equilibrium problem with constraints are obtained. Then, by using the Gerstewitz nonconvex separation functional, a necessary and sufficient condition for epsilon-vector equilibrium problem without constraints is obtained.
Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. In parti...
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Some necessary global optimality conditions and sufficient global optimality conditions for nonconvex minimization problems with a quadratic inequality constraint and a linear equality constraint are derived. In particular, global optimality conditions for nonconvex minimization over a quadratic inequality constraint which extend some known global optimality conditions in the existing literature are presented. Some numerical examples are also given to illustrate that a global minimizer satisfies the necessary global optimality conditions but a local minimizer which is not global may fail to satisfy them.
This paper presents a global optimization algorithm for solving globally the generalized nonlinear multiplicative programming (MP) with a nonconvex constraint set. The algorithm uses a branch and bound scheme based on...
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This paper presents a global optimization algorithm for solving globally the generalized nonlinear multiplicative programming (MP) with a nonconvex constraint set. The algorithm uses a branch and bound scheme based on an equivalently reverse convex programming problem. As a result, in the computation procedure the main work is solving a series of linear programs that do not grow in size from iterations to iterations. Further several key strategies are proposed to enhance solution production, and some of them can be used to solve a general reverse convex programming problem. Numerical results show that the computational efficiency is improved obviously by using these strategies.
We consider and study a new class of variational inequality, which is called the general mixed quasivariational inequality. We use the auxiliary principle technique to study the existence of a solution of the general ...
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We consider and study a new class of variational inequality, which is called the general mixed quasivariational inequality. We use the auxiliary principle technique to study the existence of a solution of the general mixed quasivariational inequality. Several special cases are also discussed. Results proved in this paper may stimulate further research in this area.
We suggest and analyze some implicit iterative methods for solving the extended general nonconvex variational inequalities using the projection technique. We show that the convergence of these iterative methods requir...
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We suggest and analyze some implicit iterative methods for solving the extended general nonconvex variational inequalities using the projection technique. We show that the convergence of these iterative methods requires only the gh-pseudomonotonicity, which is a weaker condition than gh-monotonicity. We also discuss several special cases. Our method of proof is very simple as compared with other techniques.
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