The circular cone is a pointed closed convex having hyperspherical sections orthogonal to its axis of revolution about which the invariant rotation, includes second-order as special case when rotation angle 45 degrees. Let<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="script">L</mml:mi></mml:mrow><mml:mrow><mml:mi>θ</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>denote in<mml:math...

In this paper, we study second-order optimality conditions for nonconvex set-constrained optimization problems. For a convex problem, it is well known that involve the support function of tangent set. propose two approaches establishing case. first approach, extend concept so applicable to general problems, whereas in second introduce notion directional regular cone and apply classical results duality theory. Besides conditions, novelty our approach lies systematic introduction use,...

Abstract The study of this paper consists two aspects. One is characterizing the so-called circular cone convexity f by exploiting second-order differentiability <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mi>f</mml:mi><mml:msub><mml:mi>L</mml:mi><mml:mi>θ</mml:mi></mml:msub></mml:msup></mml:math> ; other introducing concepts determinant and trace associated with establishing their basic inequalities. These results show essential role played angle θ , which gives...

The dry process for crumb rubber modified (CRM) asphalt mixtures is characterized by a simple construction that results in greater environmental benefits than the wet does. However, difficulties of compaction often lead to unstable pavement performance; therefore, its application highly restricted. This research aims investigate procedure CRM using air void content and expansion ratio as principal indices evaluation. To evaluate key factors affecting compaction, series were prepared...

In this paper we consider a mathematical program with second-order cone complementarity constraints (SOCMPCC). The SOCMPCC generalizes the (MPCC) in replacing set of nonnegative reals by cones. There are difficulties applying classical Karush--Kuhn--Tucker (KKT) condition to directly since usual constraint qualification such as Robinson's never holds if it is considered an optimization problem convex constraint. Using various reformulations and recent results on exact formula for...

.In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs. Unlike the existing results in literature, our prove to be sufficient, an essential local minimizer of second order, under merely basic smoothness and closedness assumptions on data defining problem. In part, comprehensive first- variational analysis disjunctive systems demonstrate how objects appearing can...

This paper conducts variational analysis of circular programs, which form a new class optimization problems in nonsymmetric conic programming, important for theory and its applications. First, we derive explicit formulas terms the initial problem data to calculate various generalized derivatives/co-derivatives projection operator associated with cone. Then apply differentiation other tools establish complete characterizations full tilt stability locally optimal solutions parameterized programs.

The second-order cone complementarity problem (denoted by SOCCP) can be effectively solved smoothing-type algorithms, which in general are designed based on some monotone line search. In this paper, a new smoothing function of the Fischer–Burmeister function, we propose algorithm for solving SOCCP. proposed uses nonmonotone search scheme, contains usual as special case. Under suitable assumptions, show that is globally and locally quadratically convergent. Some numerical results reported...

We consider the weighted linear complementarity problem (denoted by wLCP). Many numerical algorithms have been proposed for solving monotone wLCP. In this paper, we propose a damped Gauss–Newton method to solve non-monotone wLCP which is designed based on derivative-free line search. show that well defined and it globally convergent without any assumptions. Moreover, analyze local quadratic convergence of under non-singularity condition error bound condition, respectively. Our not only has...

The second-order tangent set is an important concept in describing the curvature of involved. Due to existence complementarity condition, cone (SOC) a nonconvex set. Moreover, unlike vector set, SOC not even union finitely many polyhedral convex sets. Despite these difficulties, we succeed showing that like directionally differentiable and exact formula for can be given. We derive results by establishing relationship between directional derivative projection operator over SOC, calculating...

In this paper, some new nonlinear delay integral inequalities on time scales are established, which provide a handy tool in the research of boundedness unknown functions dynamic equations scales. The established results generalize Lipovan [J. Math. Anal. Appl. 322, 349-358 (2006)], Pachpatte 251, 736-751 (2000)], Li [Comput. 59, 1929-1936 (2010)], and Sun 301, 265-275 (2005)]. MSC 2010: 26E70; 26D15; 26D10.