This note provides another proof for the convexity (strict convexity) of log det(I + KX) over the positive definite cone for any given positive semidefinite matrix K 0 (positive definite matrix K ≻ 0) and the strictly convexity of log det(K + X) over the positive definite cone for any given K 0. Equivalent optimization representation with linear matrix inequalities (LMIs) for the functions log ...

In multi-circular synthetic aperture radar (MCSAR) mode, resolution and sidelobes are two important parameters to consider when representing imaging quality, as in other SAR imaging modes. In this paper, three-dimensional (3-D) resolution and cone-shaped sidelobes of MCSAR are analyzed for a point target in the scene center under the Nyquist sampling criterion. The results of the analysis show ...

In this paper, we introduce the notion of a second-order coneconvex function involving second-order directional derivative. Also, second-order cone-pseudoconvex, second-order cone-quasiconvex and other related functions are defined. Second-order optimality and Mond-Weir type duality results are derived for a vector optimization problem over cones using the introduced classes of functions.

In this paper, we reformulate the stochastic generalized second-order cone complementarity problems as boxconstrained optimization problems. If satisfy the condition that the reformulation’s objective value is zero, the solutions of box-constrained optimization problems are also solutions of stochastic generalized second-order cone complementarity problems. Since the box-constrained minimizatio...

A comparison between different modern population based optimization methods applied to the design of scannable circular antenna arrays is presented in this paper. This design of scannable circular arrays considers the optimization of the amplitude and phase excitations across the antenna elements to operate with optimal performance in the whole azimuth plane (360◦). Simulation results for scann...

Copositive optimization is a quickly expanding scientific research domain with wide-spread applications ranging from global nonconvex problems in engineering to NP-hard combinatorial optimization. It falls into the category of conic programming (optimizing a linear functional over a convex cone subject to linear constraints), namely the cone C of all completely positive symmetric n×n matrices (...

Learning distance metrics from data is a fundamental problem in machine learning and useful way to extract data-driven features by using the matrix root of a distance matrix. Finding a proper metric amounts to optimization over the cone of positive definite (PD) matrices. This optimization is difficult since restricting optimization to remain within the PD cone or repeatedly projecting to the c...

In this paper, we study the circular cone eigenvalue complementarity problem (CCEiCP) by variational inequality technique, prove the existence of a solution to CCEiCP, and investigate different nonlinear programming formulations of the symmetric and asymmetric CCEiCP, respectively. We reduce CCEiCP to a variational inequality problem on a compact convex set, which guarantees that CCEiCP has at ...

Facial reduction heuristics are developed in the interest of added performance and reliability in methods for mixed-integer conic optimization. Specifically, the process of branch-and-bound is shown to spawn subproblems for which the conic relaxations are difficult to solve, and the objective bounds of linear relaxations are arbitrarily weak. While facial reduction algorithms already exist to d...