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We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
In this paper, we consider a class of nonconvex problems with linear constraints appearing frequently in the area of image processing. We solve this problem by the penalty method and propose the iteratively reweighted alternating…
Augmented Lagrangian dual augments the classical Lagrangian dual with a non-negative non-linear penalty function of the violation of the relaxed/dualized constraints in order to reduce the duality gap. We investigate the cases in which…
In this paper, we study the mathematical program with equilibrium constraints (MPEC) formulated as a mathematical program with a parametric generalized equation involving the regular normal cone. Compared with the usual way of formulating…
In this article, a model predictive control (MPC) method is proposed for constrained linear systems to track bounded references with arbitrary dynamics. Besides control inputs to be determined, artificial reference is introduced as…
We present a systematic introduction to first-order optimality conditions for mathematical programs with equilibrium constraints (MPECs), emphasizing the limitations of classical nonlinear programming techniques. The goal is twofold. First,…
This paper proposes a Riemannian Multiobjective Proximal Gradient Method (RMPGM) for composite optimization problems on manifolds. Unlike scalarization-based approaches, the proposed framework directly handles vector-valued objectives and…
The cardinality-constrained mean-variance portfolio problem has garnered significant attention within contemporary finance due to its potential for achieving low risk while effectively managing risks and transaction costs. Instead of…
This paper proposes a new method to provide the exponential convergence of both the parameter and tracking errors of the composite adaptive control system without the persistent excitation (PE) requirement. Instead, the derived composite…
In this paper, an inexact proximal-point penalty method is studied for constrained optimization problems, where the objective function is non-convex, and the constraint functions can also be non-convex. The proposed method approximately…
We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters…
When machine learning systems meet real world applications, accuracy is only one of several requirements. In this paper, we assay a complementary perspective originating from the increasing availability of pre-trained and regularly…
This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…
We consider the nonlinear optimization problem with least $\ell_1$-norm measure of constraint violations and introduce the concepts of the D-stationary point, the DL-stationary point and the DZ-stationary point with the help of exact…
This paper investigates adaptive model predictive control (MPC) for a class of constrained linear systems with unknown model parameters. This is also posed as the dual control problem consisting of system identification and regulation. We…
Many problems in machine learning can be solved by rounding the solution of an appropriate linear program (LP). This paper shows that we can recover solutions of comparable quality by rounding an approximate LP solution instead of the ex-…
A path-following collision-avoidance model predictive control (MPC) method is proposed which approximates obstacle shapes as convex polygons. Collision-avoidance is ensured by means of the signed distance function which is calculated…
In this two-part study we develop a general approach to the design and analysis of exact penalty functions for various optimal control problems, including problems with terminal and state constraints, problems involving differential…
Polynomial optimization encompasses a broad class of problems in which both the objective function and constraints are polynomial functions of the decision variables. In recent years, a substantial body of research has focused on…