Studies regarding the computation of Optimal Control Problems (OCPs) with terminal inequality constraint, under the frame of the Variation Evolving Method (VEM), are carried out. The attributes of equality constraints and inequality constraints in the generalized optimization problem is traversed, and the intrinsic relations to the multipliers are uncovered. Upon these preliminaries, the right ...

We study a general multiobjective optimization problem with variational inequality, equality, inequality and abstract constraints. Fritz John type necessary optimality conditions involving Mordukhovich coderivatives are derived. They lead to Kuhn-Tucker type necessary optimality conditions under additional constraint qualifications including the calmness condition, the error bound constraint qu...

where mj > 0, dj > 0, j ∈ J, x = (xj)j∈J, and J def = {1, . . . , n}. Denote this problem by (Q≤) in the first case (problem (1.1)–(1.3) with inequality “≤” constraint (1.2)), by (Q) in the second case (problem (1.1)–(1.3) with equality constraint (1.2)), and by (Q≥) in the third case (problem (1.1)–(1.3) with inequality “≥” constraint (1.2)). Denote by X≤, X, X≥ the feasible set (1.2)–(1.3) in...

We deal with differential conditions for local optimality. The conditions we derive for inequality constrained problems do not require constraint qualifications and are the broadest conditions based only on first and second order derivatives. A similar result is proved for equality constrained problems, although necessary conditions require regularity of the equality constraints.

Support vector ordinal regression (SVOR) is a popular method to tackle ordinal regression problems. However, until now there were no effective algorithms proposed to address incremental SVOR learning due to the complicated formulations of SVOR. Recently, an interesting accurate on-line algorithm was proposed for training ν-support vector classification (ν-SVC), which can handle a quadratic form...

We consider the geometric numerical integration of Hamiltonian systems subject to both equality and “hard” inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. Additionally, however, we also consider invariant preservation over persistent, simultaneous, and/or frequent boundary interactions. Appropriately formulating geometric met...

An unresolved debate in the development literature concerns the impact of gender inequality on economic growth. Previous studies have found that the effect varies, depending on the measure of inequality (wages or capabilities). This paper expands that discussion by considering both the shortand long-run, evaluating the effects of gender equality in two types of economies—semi-industrialized eco...

Inverse Young inequality asserts that if $nu >1$, then $|zw|ge nu|z|^{frac{1}{nu}}+(1-nu)|w|^{frac{1}{1-nu}}$, for all complex numbers $z$ and $w$, and equality holds if and only if $|z|^{frac{1}{nu}}=|w|^{frac{1}{1-nu}}$. In this paper the complex representation of quaternion matrices is applied to establish the inverse Young inequality for matrices of quaternions. Moreover, a necessary and ...