Related papers: Lagrange Multiplier Local Necessary and Global Suf…
In this note, we prove that minimizers of convex functionals with a convexity constraint and a general class of Lagrangians can be approximated by solutions to fourth-order equations of Abreu type. Our result generalizes that of Le (Twisted…
We propose a semi-proximal augmented Lagrangian based decomposition method for convex composite quadratic conic programming problems with primal block angular structures. Using our algorithmic framework, we are able to naturally derive…
Computing the discrete rational minimax approximation in the complex plane is challenging. Apart from Ruttan's sufficient condition, there are few other sufficient conditions for global optimality. The state-of-the-art rational…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
In this paper, we consider the quadratic programming problems under finitely many convex quadratic constraints in Hilbert spaces. By using the Legendre property of quadratic forms or the compactness of operators in the presentations of…
Recent strides in nonlinear model predictive control (NMPC) underscore a dependence on numerical advancements to efficiently and accurately solve large-scale problems. Given the substantial number of variables characterizing typical…
We consider a convex minimization problem for which the objective is the sum of a homogeneous polynomial of degree four and a linear term. Such task arises as a subproblem in algorithms for quadratic inverse problems with a…
Using the recent weighted generalized fractional order operators of Hattaf, a general fractional optimal control problem without constraints on the values of the control functions is formulated and a corresponding (weak) version of…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…
In the context of augmented Lagrangian approaches for solving semidefinite programming problems, we investigate the possibility of eliminating the positive semidefinite constraint on the dual matrix by employing a factorization. Hints on…
In this paper, we develop a unified framework able to certify both exponential and subexponential convergence rates for a wide range of iterative first-order optimization algorithms. To this end, we construct a family of parameter-dependent…
We revisit the problem of approximating minimizers of certain convex functionals subject to a convexity constraint by solutions of fourth order equations of Abreu type. This approximation problem was studied in previous works of…
Hypergraph matching is a fundamental problem in computer vision. Mathematically speaking, it maximizes a polynomial objective function, subject to assignment constraints. In this paper, we reformulate the hypergraph matching problem as a…
The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally…
We consider the problem of minimizing the sum of a Lipschitz differentiable convex function $f$ and a proper closed convex function $h$ that admits efficient linear minimization oracles, subject to multiple smooth convex inequality…
In this paper we present a complete iteration complexity analysis of inexact first order Lagrangian and penalty methods for solving cone constrained convex problems that have or may not have optimal Lagrange multipliers that close the…
Based on a characterization of the optimality of a feasible solution of a convex entropy minimization problem, one shows that the feasible solutions obtained using formally the Lagrange multipliers method are optimal.
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are…
Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
This paper provides a theoretical and numerical investigation of a penalty decomposition scheme for the solution of optimization problems with geometric constraints. In particular, we consider some situations where parts of the constraints…