This paper describes and demonstrates a new and highly innovative technique that identifies an approximation of the entire bounding surface of the feasible objective region directly, including deep concavities, disconnected regions and the edges of interior holes in the feasible areas. The Pareto front is a subset of the surface of the objective boundary and can be extracted easily. Importantly...

ABSTRACT The phenomenon consisting in all the feasible region of a multiple objective linear programming problem being weakly efficient, may be less unlikely than has been believed, particularly for problems whose feasible regions have no interior. To deal with such possibility of complete weak efficiency, we would want to have at our disposal proficient methods to check this situation. So, in ...

Pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space. Tbat is, at any iteration, the hext point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence. Th...

We develop an affine-scaling algorithm for box-constrained optimization which has the property that each iterate is a scaled cyclic Barzilai–Borwein (CBB) gradient iterate that lies in the interior of the feasible set. Global convergence is established for a nonmonotone line search, while there is local R-linear convergence at a nondegenerate local minimizer where the second-order sufficient op...

We introduce a framework in which updating rules for the barrier parameter in primal-dual interior-point methods become dynamic. The original primal-dual system is augmented to incorporate explicitly an updating function. A Newton step for the augmented system gives a primal-dual Newton step and also a step in the barrier parameter. Based on local information and a line search, the decrease of ...

Fig. 1. Visualizations of the hemoglobin molecule undergoing dynamic deformation as oxygen binds to it. (a) A primal space visualization of the first time step with the heme group identified. (b) Visualization of the complementary space of the first time step shows the geometry of the interior. The surface has been made transparent, revealing a large tunnel through the surface (yellow) with man...

In the paper a primal-infeasible interior point algorithm is proposed for linearly constrained convex programming. The starting point is any positive primal-infeasible dual-feasible point in a large region. The method maintains positivity of the iterates which point satisfies primalinfeasible dual-feasible point. At each iterates it requires to solve approximately a nonlinear system. It is show...

The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon If the basic reproduction number R is below unity the disease free equilibrium P is globally stable in the feasible region and the disease always dies out If R a unique endemic equilibrium P is globally asymptotically stable in the interior of the feasible regi...

Introduction: Total hip arthroplasty (THA) after proximal femoral fixation is a challenging procedure due to possible hardware-related complications. Case presentation: A 78-year-old female with hip osteoarthritis had a proximal femoral osteotomy fixed using a blade plate in the same femur 41 years ago. A two-step approach was planned. After a challenging...

Abstract We generalize a primal-dual interior-point algorithm (IPA) proposed recently in (Illés T, Rigó PR, Török R Unified approach of algorithms for new class AET functions, 2022) to $$P_*(\kappa )$$ P ∗ ( κ <m...