Tuy, H. , Global Minimization of a Difference of Two Convex Functions , Mathematical Programming Study, Vol. 30, pp. 250–282, 1987.H. Tuy. Global minimization of a difference of two convex functions. Mathematical Programming Study 30 (1987) 150-187....
Difference of quasiconvex functionsQ-subdifferentialOptimality conditionsIn this note, we are concerned with an optimization problem (P) where the objective function is the difference of two quasiconvex functions. Using a suitable subdifferential introduced by Suzuki and Kuroiwa (Nonlinear Anal 74:1279–...
A DC decomposition of the above objective function DC Formulation For all with A Question: is H(T, V) unconditionally convex? No! Condition ensuring H(T,V) Notice here B denotes a Ball and thus is convex! In fact, alpha can be 2 max{‖xk‖, k=1, 2, …, n} ! Proof (1) Proo...
Melzer, D. (1986), On the Expressibility of Piecewise-Linear Continuous Functions as the Difference of two Piecewise-Linear Convex Functions. Math. Programming Study 29 , pp. 118 — 134.D. Melzer. On the expressibility of piecewise-linear continuous functions as the difference of two piecewise-...
c. optimization problem on a convex set. The objective function is represented as the difference of two convex functions. By reducing the problem to the equivalent concave programming problem we prove a sufficient optimality condition in the form of an inequality for the directional derivative of ...
The nonconvex constrained minimization problem for a differentiable function that can be written as the difference of two convex functions is examined. Global optimality conditions are given for a point and a minimizing sequence. A global search strategy based on these conditions is developed, and it...
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However, the performance of AdaGrad is deteriorated with dense gradients and nonconvex objective functions [31]. Consequently, we explore the integration of neural TD with Adam-type algorithms, which stand out as more potent tools for training deep neural networks owing to their superior performance...
We improve this result by constructing a delta convex function of class $C^1(\Bbb R^2)$ which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable...
We show that the class of all delta-convex selfmappings of R (differences of two convex functions) enjoys the difference property in the sense of N.G. de Bruijn. The Q-differentiability technique has been applied as a proof tool. (C) 2013 Royal Dutch Mathematical Society (KWG). Published...