No Gap Second-Order Optimality Conditions for Circular Conic Programs

On equilibrium multivalued problems in the general model with the Boolean-valued bifunction

“…14);(2,13);(2,15)}.It implies that Φ(x, y)+Φ(x, y) / ∈ 1 2αq−coreC. Hence, the condition (i) of Theorem 4.13 is fulfilled.…”

“…Let E and F be two non-empty sets and given a bifunction Φ : E × F → R. The problem which consists of finding an element x ∈ E satisfying Φ(x, y) ≥ 0 for all y ∈ F(1)has been studied previously in the works of Ky Fan [6], Muu and Oettli [18], Blum and Oettli [2] and others, with the term "equilibrium problem" (in short, EP Φ ). This problem and its related topics play important roles in many different areas of sciences, such as electrical circuits, economics, finance, game theory, constrained optimization, traffic network equilibrium problem, etc (see, e.g., [1,5,15,17,[19][20][21]). The variations of the problem (EP Φ ) are often considered with convex assumptions in a topologically structured environment, such as, in [15], the authors study the second-order optimality conditions for a class of the circular conic optimization problem, in that, the explicit expressions of the tangent cone and the second-order tangent set are established to discuss the minimal problems.…”

“…This problem and its related topics play important roles in many different areas of sciences, such as electrical circuits, economics, finance, game theory, constrained optimization, traffic network equilibrium problem, etc (see, e.g., [1,5,15,17,[19][20][21]). The variations of the problem (EP Φ ) are often considered with convex assumptions in a topologically structured environment, such as, in [15], the authors study the second-order optimality conditions for a class of the circular conic optimization problem, in that, the explicit expressions of the tangent cone and the second-order tangent set are established to discuss the minimal problems. In the work [16], the authors study the solubilities of optimization problems associated with the secondorder cone.The study of EP Φ has been extended from scalar to the vector case (for instance, [3,20] and the references therein).…”

“…has been studied previously in the works of Ky Fan [6], Muu and Oettli [18], Blum and Oettli [2] and others, with the term "equilibrium problem" (in short, EP Φ ). This problem and its related topics play important roles in many different areas of sciences, such as electrical circuits, economics, finance, game theory, constrained optimization, traffic network equilibrium problem, etc (see, e.g., [1,5,15,17,[19][20][21]).…”

“…The variations of the problem (EP Φ ) are often considered with convex assumptions in a topologically structured environment, such as, in [15], the authors study the second-order optimality conditions for a class of the circular conic optimization problem, in that, the explicit expressions of the tangent cone and the second-order tangent set are established to discuss the minimal problems. In the work [16], the authors study the solubilities of optimization problems associated with the secondorder cone.…”