Related papers: A second-order sequential optimality condition for…
Optimization theory in Banach spaces suffers from the lack of available constraint qualifications. Despite the fact that there exist only a very few constraint qualifications, they are, in addition, often violated even in simple…
This paper extends the SQP-approach of the well-known bundle-Newton method for nonsmooth unconstrained minimization to the nonlinearly constrained case. Instead of using a penalty function or a filter or an improvement function to deal with…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
We study local controllability and optimal control problems for invertible discrete-time control systems. We present second order necessary conditions for optimality and sufficient conditions for local controllability. The conditions are…
Most existing work focuses on the generalization of KKT for nonsmooth convex optimization problems, but this paper explores a generalized form of Karush-Kuhn-Tucker (KKT) conditions for real continuous optimization problems.
Standard H-infinity/H2 robust control and analysis tools operate on uncertain parameters assumed to vary independently within prescribed bounds. This paper extends their capabilities in the presence of constraints coupling these parameters…
Training learned image compression (LIC) models entails navigating a challenging optimization landscape defined by the fundamental trade-off between rate and distortion. Standard first-order optimizers, such as SGD and Adam, struggle with…
The numerical performance of algorithms can be studied using test sets or procedures that generate such problems. This paper proposes various methods for generating linear, semidefinite, and second-order cone optimization problems.…
This paper considers a nonconvex optimization problem that evolves over time, and addresses the synthesis and analysis of regularized primal-dual gradient methods to track a Karush-Kuhn-Tucker (KKT) trajectory. The proposed regularized…
The paper is devoted to obtain first and second order necessary optimality conditions for continuous-time optimization problems with equality and inequality constraints. A full rank type regularity condition along with an uniform implicit…
This paper provides second-order optimality conditions for optimization problems with generalized equation constraints (GEPs), a framework that encompasses several important and challenging models in mathematical programming, including…
In this paper, we study the linear complementarity problems on extended second order cones. We convert a linear complementarity problem on an extended second order cone into a mixed complementarity problem on the non-negative orthant. We…
For linear time-invariant (LTI) systems, the design of an optimal controller is a commonly encountered problem in many applications. Among all the optimization approaches available, the linear quadratic regulator (LQR) methodology certainly…
In this paper, we obtain a new proof of Fritz John necessary optimality conditions for vector problems applying Kakutani fixed point theorem and Hadamard directional derivative. We also derive a similar proof of second-order Fritz John…
In this paper, a robust sequential quadratic programming method for constrained optimization is generalized to problem with an {expectation} objective function {and} deterministic equality and inequality constraints. A stochastic line…
In this paper, we readdress the classical topic of second-order sufficient optimality conditions for optimization problems with nonsmooth structure. Based on the so-called second subderivative of the objective function and of the indicator…
A simple characterization of the solvability of power flow equations is of great importance in the monitoring, control, and protection of power systems. In this paper, we introduce a sufficient condition for power flow Jacobian…
We consider the problem of optimizing the state average of a polynomial of non-commuting variables, over all states and operators satisfying a number of polynomial constraints, and over all Hilbert spaces where such states and operators are…
This paper is concerned with the derivation of first- and second-order sufficient optimality conditions for optimistic bilevel optimization problems involving smooth functions. First-order sufficient optimality conditions are obtained by…
The second-order tangent set is an important concept in describing the curvature of the set involved. Due to the existence of the complementarity condition, the second-order cone (SOC) complementarity set is a nonconvex set. Moreover,…