Published in Journal of Optimization Theory and Applications
Subvexormal functions and subinvexormal functions are proposed, whose properties are shared commonly by most generalized convex functions and most generalized invex functions, respectively. A necessary and sufficient condition for a subvexormal function to be subinvexormal is given in the locally Lipschitz and regular case. Furthermore, subvex func...
6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to th...
Published in Journal of Optimization Theory and Applications
In this paper, a class of global optimization problems is considered. Corresponding to each local minimizer obtained, we introduced a new modified function and construct a corresponding optimization subproblem with one constraint. Then, by applying a local search method to the one-constraint optimization subproblem and using the local minimizer as ...
Published in Journal of Optimization Theory and Applications
We present a unified approach to establishing the existence of global minima of a (non)convex constrained optimization problem. Our results unify and generalize previous existence results for convex and nonconvex programs, including the Frank-Wolfe theorem, and for (quasi) convex quadratically constrained quadratic programs and convex polynomial pr...
Optimization problems with cardinality constraints are very difficult mathematical programs which are typically solved by global techniques from discreteoptimization. Here we introduce a mixed-integer formulation whose standard relaxation still has the same solutions (in the sense of global minima) as the underlying cardinality-constrained problem; t...
Optimization problems with cardinality constraints are very difficult mathematical programs which are typically solved by global techniques from discrete optimization. Here we introduce a mixed-integer formulation whose standard relaxation still has the same solutions (in the sense of global minima) as the underlying cardinality-constrained problem...
Published in Russian Journal of Inorganic Chemistry
The GaxO (x = 2–4) clusters were studied using density functional theory (B3PW91). The global minima contain linear dicoordinate, T-shape tricoordinate and planar tetracoordinate oxygen for Ga2O, Ga3O and Ga4O, respectively. The 18-electron rule and preference for planar structure for Ga4 contribute to square structure for Ga4O. NICS values reveal ...
Published in Journal of Structural Chemistry
AbstractThe clusters InxO (x = 2, 3) and In4O0/—1 arestudied using density functional theory (B3PW91). The global minima contain linear di-coordinated, T-shape tri-coordinated, and planar tetra-coordinated oxygen atoms for In2O, In3O, and In4O, respectively. 18-valence electrons contribute to square structure of In4O. Excitingly, 19-valence electro...
